The King's niece announced that the newest member of her family was delivered in a hospital in Lisbon and weighed 6lbs 9oz.
Posting on Instagram, Eugenie said she and husband Jack Brooksbank were "beyond in love with our girlie".
Both mother and baby are said to be doing well.
The couple already have two boys, five-year-old August and three-year-old Ernest.
It's understood they are taking their time to choose a name for their daughter - who is now 15th in line to the throne, just ahead of Eugenie's uncle, Prince Edward.
However the baby girl, who will be the 15th great-grandchild of the late Queen and the third born since her death in 2022, will not be a HRH.
Buckingham Palace said the couple were "delighted to announce the safe arrival of their daughter" - born on 3 August at 6.20pm.
"Their Majesties The King and Queen and other members of the royal family were delighted to be informed of the news," the statement added.
The birth is a rare occasion where a member of the royal family who is in the direct line of succession has been born overseas.
Princess Lilibet who lives in California with her parents, Prince Harry and Meghan Markle, was the previous member of the family born outside the UK.
The last monarch to be born abroad was George II who, as one of the Hanoverian kings, was born in what is now northern Germany.
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The new arrival is Andrew Mountbatten-Windsor's fifth grandchild - as Princess Beatrice has two girls and a stepson with her husband Edoardo Mapelli Mozzi.
Currently Eugenie and her husband are spending much of their time in Portugal, where they own a home.
They are understood to use Ivy Cottage, a three-bedroom property in the grounds of Kensington Palace, when back in the UK.
It is not known at which hospital the baby was delivered, but the couple are said to be "deeply grateful" to the medical staff for their care.
Eugenie's pregnancy was announced in May, with the princess sharing on Instagram a picture of her young son Ernest, wearing a Chelsea football kit, and her other child August, wearing a long-sleeved grey T-shirt, holding a picture of a baby scan.
The upper stage of a SpaceX Falcon 9 rocket, launched 19 months ago before unintentionally veering towards the moon, is set to collide with an explosive impact equivalent to three tons of TNT.
Space-tracking expert Bill Gray predicts an impact speed of 5,400mph - seven times the speed of sound - when the object hits near Einstein Crater on the moon's sunlit western limb.
While NASA spokesperson Jimi Russell has said that "there is no danger to Earth" from the impact, eyes around the world will be looking for the moment the spacecraft crashes.
When is it due to crash?
We don't know the exact minute, but the collision is expected to take place at around 2.35am Eastern Time - so around 7.35am in the UK - on Wednesday morning.
Even if it's dark out, the view of the impact flash will be too dim to see the moment of impact. However, it may be visible by telescope for tens of minutes.
The eastern portions of the US and Canada, and much of South America, should have the best views.
What do scientists expect will happen?
Nothing catastrophic, but scientists say the moment of impact will be massive, carving out a crater and sending up a plume of dust and rubble.
NASA's Lunar Reconnaissance Orbiter and South Korea's Danuri lunar orbiter will gather before-and-after shots of the crash scene.
Another scientist, Benjamin Fernando, from the Los Alamos National Laboratory in New Mexico, echoed this, saying: "The gravity on the moon is low and there is no wind to blow the dust away."
In the aftermath, he anticipates an impact crater nearly 90ft (27m) across and 16ft (5m) deep - too small to see from Earth but visible to spacecraft.
But both said that they aren't too concerned about the impact itself.
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So what are they concerned about?
Concerns are more about the amount of space debris in the Earth's orbit - where, as of July, the European Space Agency suggests there are more than one hundred million pieces of small objects.
Mr Fernando said that "part of the reason for our interest in this event is to figure out how much of a hazard debris impacts pose to future astronauts".
And Mr Gray added: "Things are getting crowded up there."
Detritus from man-made objects falls from orbit on occasion
In October last year, a burning piece of space debris that crashed to Earth was found by mine workers nearly 19 miles east of Newman, Western Australia.
And last May, a car-sized piece of the Soviet rocket Cosmos 482 crashed back to Earth after 53 years in orbit.
What do we know about the rocket?
SpaceX's Falcon 9 is a partially reusable, two-stage rocket - with this specific rocket launched as part of a US and Japanese mission to carry a pair of lunar landers and scientific equipment to the moon last year.
While the concept is to make the rocket reusable and returnable to Earth for future missions, part of the Falcon 9 is shed in orbit, where it remains, unless collided with.
The part on track for the moon is the upper stage of the rocket - about the size of a five-storey building, with a weight on Earth of at least 4,000kg.
Has this happened before?
Yes, SpaceX's Falcon 9 will be the second dead rocket to crash into the moon by accident.
The first came when a Chinese rocket segment dug out a pair of craters on the lunar far side in 2022.
At the time, Mr Gray said it was likely the third stage of a Chinese rocket that sent a test sample capsule to the moon and back in 2014.
Chinese ministry officials said the upper stage had reentered Earth's atmosphere and burned up.
A 2023 study in the Planetary Science Journal said it found "conclusively" that the debris was from China's Long March 3C rocket from a 2014 lunar mission.
More than 300 Palestinians were killed on 22 November 2023, less than two months into the Israel-Hamas war, in an airstrike in Gaza City's Sabra neighbourhood.
About 40 bodies were recovered in the immediate aftermath, but most were buried too deep.
Gaza's civil defence agency said other victims were located this past weekend by emergency workers who dug through the destroyed buildings to retrieve the remains of 112 people, including 40 children.
It added that 157 bodies have still not been found.
"The only crime of these martyrs was that they remained steadfast and resilient in their homes," one relative, Taysir al Hassayna, told AP news agency.
For the missing, it's "as if their bodies had evaporated without a trace", al Hassayna added.
Many people killed in the war - which started after Hamas's terror attack on Israel - are only now being recovered from countless ruined buildings.
At least 7,400 people have been reported by relatives as still being buried in rubble, according to Gaza's health ministry.
Its head of records, Zaher al-Waheidi, said the true figure is likely to be thousands higher as in many cases whole families were killed, leaving no one to report the missing.
Israel insists it has not deliberately targeted civilians and that those killed are as a result of Hamas embedding itself among Gaza's densely packed population.
However, critics claimed efforts to avoid civilians have been either non-existent or woefully lacking.
Gaza's health ministry - which is under the Hamas-led government - says more than 73,000 people have been killed since the war began.
The conflict started after Hamas stormed into Israel on 7 October 2023, killing around 1,200 people and taking 251 hostages.
Scattered petals and photos
Those mourned on Tuesday were from an apartment block belonging to the Hassayna and Abu Sharia clan.
The remains were wrapped in Palestinian flags and laid in rows. Many were marked with a photo and petals were scattered.
Hundreds of people gathered around the remains to pray before the bodies were carried on stretchers down a narrow street to be buried at a nearby cemetery.
An Israel-Hamas ceasefire began in October 2025 but both sides accuse each other of breaching it. Gaza's health ministry says at least 1,252 have been killed since it came into effect.
Israel says its strikes are against militants who threaten its soldiers, against those involved in the October 2023 terror attack, or who carry out other violations.
Five Israeli soldiers have also been killed since the ceasefire started.
The future of Gaza and hopes of rebuilding it remain fragile. Hamas has kept its weapons despite agreeing to disarm, while Israel has refused to withdraw and still controls half the territory.
A new disarmament deal is in the works via America's Board of Peace initiative, but Gaza remains in a shattered, desperate state.
Most of its two million people are displaced and many are still living in overcrowded and unsanitary tent camps plagued by rats and outbreaks of diseases like chickenpox.
Police said the killing took place in Calcutt, near Cricklade, at about 8.15am on Sunday, and that a total of five suspects have so far been arrested in connection with the death.
The victim - named by police as Jimmy Ward, 36 - was declared dead at the scene.
Officers said the suspect was arrested on Tuesday.
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The others taken into custody included two men, aged 53 and 29, who were arrested on suspicion of assisting an offender after a car was pulled over on the nearby A419 on Tuesday.
On Sunday, a 74-year-old man and 42-year-old woman were arrested on suspicion of assisting an offender and possession of a firearm.
All five people are in custody for questioning, Wiltshire Police said.
Detective Chief Inspector Phil Walker, the senior investigating officer, said: "Jimmy's next of kin have been informed of this development and my thoughts continue to be with them. They are being supported by specially trained officers.
"A scene and heavy policing presence remain in place at the Traveller site in Calcutt while further inquiries are carried out. I continue to ask that this cordon is respected."
The girl died after being taken to Ninewells Hospital in Dundee by ambulance, while three members of her family were also treated there as a precaution before being discharged.
The suspect was taken separately to the same hospital by police. He was discharged and is now in custody.
Emergency services were called to reports of a serious incident at Elliot Industrial Estate in Arbroath at around 11.53pm on Sunday.
Police Scotland said the nine-year-old girl was found with serious injuries and later died in hospital.
A 35-year-old man has been arrested in connection with her death and remains in custody.
Detectives said the girl and man were known to one another and there is no wider risk to the public.
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The Scottish Ambulance Service said: "We received a call at 23:53 on Sunday 2 August to attend an incident at Elliot Industrial Estate, Arbroath.
"We dispatched four ambulance response vehicles to the scene and we transported four patients to Ninewells Hospital."
Flowers have been laid at the scene, which is currently cordoned off while specialist officers examine the area.