The Northern Ireland-born New Zealand actor was best known for his leading roles in the blockbuster dinosaur franchise and The Piano, and appeared in more than 50 films over his career.
The family of the screen star, who was one of New Zealand's most successful Hollywood exports, said his death had been "sudden and unexpected" in a statement on Monday.
Neill was diagnosed with stage three angioimmunoblastic T-cell lymphoma, a rare type of non-Hodgkin lymphoma in 2022. His family said he had been "cancer free" when he died.
"It is with immense sadness that the whānau of Sam Neill share the news of his passing on Monday 13th July, in Sydney Australia," his family said in a statement.
"Sam was surrounded by family and passed with the dignity that has characterised his whole life.
"The loss was sudden and unexpected but blessed by the fact that Sam remained cancer free.
"They would like to express their deepest gratitude to the staff at St Vincent's Private Hospital for their incredible care.
"More details will be shared later, but for now, on behalf of the family, we ask that you respect their privacy as they navigate this immeasurable loss."
After his cancer diagnosis, Neill said he would take a short break from acting, and had announced he was cancer-free earlier this year.
Neill was regarded as a talented and versatile actor, who had traversed blockbuster and and art house film throughout his career.
His range saw him dodge velociraptors in Jurassic Park, chop off Holly Hunter's finger in The Piano and poke out his own eyes in the sci-fi film Event Horizon in his on screen roles.
Australian Prime Minister Anthony Albanese paid tribute to Neil as "wry and dry, thoughtful and laconic".
"Sam Neill starred in so many beloved Australian stories and he earned a special place in Australian hearts," he said on X.
"Wry and dry, thoughtful and laconic, Sam fought illness with the same dignity, humour and conviction that gave strength to his every performance. He will be much mourned and long remembered. May he rest in peace."
Neill was one of a host of actors and directors who achieved international fame after an explosion of Australian films that began in the late 1970s, including Paul Hogan, Mel Gibson, Geoffrey Rush, Russell Crowe, Jane Campion, Peter Weir and Gillian Armstrong.
He first came to the attention of international audiences in Armstrong's 1979 film My Brilliant Career, which also introduced Judy Davis.
He later appeared in Phillip Noyce's 1989 thriller Dead Calm, which co-stars a then-relatively unknown Nicole Kidman.
Neill twice co-starred with Meryl Streep, in Australian director Fred Schepisi's Plenty and - again for Schepisi - in A Cry in the Dark based on the true story of a dingo killing a baby in the Australian Outback.
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A 28-year-old white British male is in custody after being arrested on Saturday.
Assistant Chief Constable Matt Longman provided additional details on the investigation at a press briefing on Sunday (12 July) morning, telling media the arrest took place in Rotherham.
There is still "nothing to suggest" it is a terrorism related or politically motivated crime, he added. "And at this point, we are not looking for anyone else in connection with this murder."
ACC Longman also said more than 120 tips from the public have been received since a police appeal for information.
Ms Widdecombe was found dead at her home in Haytor, on the edge of Dartmoor, at around 11.40am on Thursday.
Police believe the former Conservative minister was attacked at around 12.30pm on Wednesday - nearly 24 hours before her body was discovered with "serious injuries".
Devon and Cornwall Police said: "We can confirm that a 28-year-old man was arrested at an address in the South Yorkshire area this evening (July 11) on suspicion of the murder of Ann Widdecombe.
"The suspect, who is a white British national, is now in police custody."
The force said that it was supported by Counter Terrorism Policing North East, while South Yorkshire Police carried out the arrest, but added there is "still no information to suggest that this is a terrorism-related incident".
A 26-year-old man initially arrested by the force on suspicion of the murder of Ms Widdecombe was released from custody on Saturday, with police stating that he was no longer part of their investigation.
Ms Widdecombe served as a Conservative MP from 1987 to 2010.
She then returned to frontline politics as a prominent voice in the Vote Leave campaign ahead of the 2016 EU referendum, before joining the Brexit Party in 2019, serving as a Member of the European Parliament.
Ms Widdecombe joined Reform UK in 2023, and became the party's immigration and justice spokesperson.
Reform MPs given extra security
Nigel Farage visited Devon to lay a wreath for Ms Widdecombe on Saturday as it was confirmed Reform MPs have been given 24-hour security, paid for by the party, for fear of similar attacks.
Mr Farage said in a tribute on Friday that Ms Widdecombe's death was "a terrible reflection on modern Britain".
"And I do fear that for anybody in public life, or especially the political space, things have become even more dangerous to them," he added.
Widdecombe's missed TV appearance
As the police piece together the timeline of Ms Widdecombe's death, it was revealed that the former MP had missed a planned TV interview on Wednesday afternoon.
She had appeared on Mark Dolan's TalkTV programme earlier in the day, and was due to feature on Matt Allwright's Channel 5 show.
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WhatsApp messages published by ITV appear to show Ms Widdecombe stopped responding to messages from a producer on the programme around the time police believe the attack took place.
She last sent a message at 12.19pm, acknowledging she had received a Zoom link, but did not respond when she was asked to join the call at 12.48pm.
The 93-year-old woman was among eight people admitted to hospital following the blaze, four of them with serious injuries.
The Andalusian regional government said the woman, who had pre-existing medical conditions, had been admitted to hospital on Friday morning with burns covering 20% of her body.
Regional emergency chief Antonio Sanz expressed condolences to the family of the woman and others killed in the wildfire, which burned more than 7,000 hectares (17,300 acres) in Los Gallardos in Almeria province when it broke out on Thursday.
Authorities have not yet formally identified any of the dead victims.
Sky News has contacted the Foreign, Commonwealth and Development Office for comment.
Spain's forensic services data unit, the CID, said that two more people had been reported missing after it started working with authorities in Britain, France and Belgium to formally register their cases, bringing the total to 10.
It said it was now allowing family members overseas to report their loved ones missing and provide DNA samples in their countries of origin, and it expected to receive more reports in the coming days.
Authorities said the dead may include some of the individuals reported as missing.
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Most of the victims are believed to be British and Belgian nationals.
Belgian businessman Stanislas Verdonckt died as the fire advanced on the mountain village of Bedar, just north of Los Gallardos, according to his son, Thomas-Wolf Verdonckt.
Authorities have said those who died ignored advice telling them to shelter in place, but Mr Verdonckt said his father was not told the fire was heading his way, or that it would be safer to stay at home.
The president of the regional government of Andalusia, Juanma Moreno, said at around midday on Sunday that the fire had been contained and its perimeter secured.
More than 1,000 residents were given the all-clear to return to their homes in the evacuated villages north of Los Gallardos on Sunday afternoon.
Mr Moreno urged citizens to remain vigilant throughout the summer, noting that in Andalusia, Spain's most populous region, an average of 15 forest fires were breaking out every day, rising at times to as many as 22.
Spanish Prime Minister Pedro Sanchez is due to visit the affected area on Monday.
Firefighters say they are working to protect communities from the fire near Sychnant Pass on Conwy Mountain.
The news comes with a huge swathe of the UK is at risk of "exceptional" wildfires this week, according to Natural England.
Dave Swallow, the National Fire Chief's Council's wildfire tactical advisor, told Sky News firefighters are currently tackling 19 wildfires across England and Wales and said strong winds following the prolonged dry weather are "exacerbating the challenge".
Jami Jennings, from North Wales Fire and Rescue Service, said: "Firefighters remain on scene working in challenging conditions to contain the fire and protect surrounding communities, property, infrastructure and the environment...
"Due to the size and complexity of the incident, operations are expected to continue for some time."
See the weather forecast for your area
He added: "We would ask members of the public to avoid the affected area to allow emergency services to work safely and efficiently. Please follow any road closures, evacuation advice or safety instructions issued by the emergency services.
"Residents in nearby communities of Dwygyfylchi and Penmaenmawr should keep windows and doors closed if affected by smoke and seek medical advice if they experience breathing difficulties. Motorists are advised to expect delays and consider alternative routes."
North Wales Police are overseeing the evacuation residents living nearby.
There is concern about the heatwave leading to wildfires elsewhere in the country.
The Fire Severity Index measures how severe a blaze could be, going from level one (low) to level five (exceptional).
The forecast for the coming days shows the likely fire severity is "very high" across most of England - and by Thursday (16 July), a huge swathe of the country will be in the top category.
Information on wind speed, temperature, time of year and rainfall is used to produce the forecasts, along with weather data from the Met Office.
Derbyshire Fire and Rescue has been called out to two moorland wildfires in recent days, while some London rail lines were closed on Friday evening after a blaze involving shrubbery at Stratford station.
On Saturday, teams tackled a fire at Devil's Dyke in South Downs National Park, West Sussex, and firefighters in East Sussex were called out to a "large fire in the open" on the South Downs near Eastbourne.
The scorching heatwave conditions being experienced by much of the UK are due to last into the coming week, with most areas expected to stay dry, sunny and very hot.
Mr Swallow warned that such conditions "significantly increase wildfire risk" but said almost all are started by people - either deliberately or accidentally.
"Whether it is a disposable barbecue left behind, a discarded cigarette, or even a glass bottle left in the sunshine, we all have a role to play in preventing them," he said.
Heat-health alerts issued by the UK Health Security Agency (UKHSA) were extended on Saturday.
Amber alerts for the West Midlands and South West, and yellow alerts for the East Midlands, the North West, the South East, the East of England and London, will remain in place until 9pm Wednesday.
The UKHSA said significant impacts are likely across health and social care services, and warned of a potential increase in water-related incidents across England, including cold water shock and drowning.
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Wildfires have raged across southern Europe in the past week.
Firefighters in southeastern Spain are still battling a blaze that started on Thursday - which has so far killed 12 people, with a further 23 missing - while several wildfires are ongoing amid soaring temperatures in France, where a firefighter has died.
The blaze near Vallentin Road and Shernhall Street has affected two houses, around 30 gardens and sheds as well as a railway embankment, London Fire Brigade (LFB) said.
People in the area were advised to keep their windows and doors closed due to a "significant amount of smoke", but the advice has since been lifted with the fire being brought under control by 10.35pm.
Motorists were also advised to avoid the area, and the Weaver Overground railway line was partially closed.
More than 100 calls were made to the fire service from around 6.30pm on Sunday.
Local MP Stella Creasy said there had been "an electrical fire on the train lines", but LFB said the cause of the blaze is unknown.
"We have got a major incident in Wood Street," she said. "There is a serious fire with a lot of roads and people being evacuated."
LFB said two rest centres have been set up for residents affected by the fire, which in a later update Ms Creasy said were being closed down as most residents were allowed to return home.
She said there were no known injuries, while most properties in the area had not been damaged, although there has been damage to sheds and gardens.
LFB Assistant Commissioner Tom Goodall said: "The Brigade will retain a significant presence on the scene through the night, working to fully extinguish the fire."