The deputy first minister at the Stormont executive will attend a cross-border event in Belfast on Wednesday, which Irish President Michael Higgins will also attend.
Sinn Fein president Gerry Adams said the decision had been taken after consulting with grass roots support and allowing the party's ruling council, the ard comhairle, to decide at a four-hour meeting in Dublin.
"This will understandably cause difficulties for some republicans and nationalists," Mr Adams said.
"Especially for those folks who suffered at the hands of British forces."
He went on to say the decision was "the right thing to do at the right time and for the right reasons".
Mr Adams said Sinn Fein wanted to see a new republic in which the traditions of orange and green could be brought together in a cordial union.
The ard comhairle decision was not unanimous but was a clear majority, the party confirmed.
Leading cross border charity Co-operation Ireland is to host an event for the Queen and Mr Higgins to celebrate the arts and culture across the island.
There has been speculation since the Queen's momentous visit to Ireland in May last year that a senior Sinn Fein figure would meet her at an event.
Mr McGuinness, a former IRA commander, was always the candidate to shake the Queen's hand but delicate talks have been going on for months to arrange a suitable venue and occasion.
The Queen has never met a senior figure in the now-defunct IRA, which killed her cousin Lord Mountbatten in 1979, or its political wing Sinn Fein.
The party decided on Friday to sanction the meeting that would have seemed inconceivable a generation ago.
Sinn Fein have stressed the meeting is not a celebration of the Jubilee.
The NI deputy first minister, a chief negotiator for Sinn Fein during tough talks to bring the IRA terror campaign to an end, turned down an invitation to meet the Queen during her visit to Ireland last year.
During her trip, the Queen won over many people by paying her respects to Ireland's patriot dead at the Garden of Remembrance in Dublin, among many other significant engagements.