Before now, it hasn’t been clear whether the two would meet in public or private, but they will today meet at the Lyric Theatre in Belfast.
Mr McGuiness is the republican former head of the IRA. He is now the leader of a more-moderate Sinn Fein, and previously declined the chance to meet the Queen, whom he had previously viewed as an enemy.
The meeting has been organised by Northern Irish charity Co-Operation Ireland, which works to bring divided communities together. Today’s event at the Lyric is being seen as a celebration in how the arts have played their part in reducing division in the region.
Today’s truce has not been welcomed by everyone in Northern Ireland however. There were minor protests in Belfast last night, and many republicans have spoken of their distaste at Mr McGuiness’ actions today.
After the event at The Lyric, the Queen and Prince Philip will then move to Stormont for a celebration of the Queen’s diamond jubilee, organised by the Northern Ireland Office.
Around 20,000 people are expected to take part in this celebration.
Yesterday, the royal couple visited relatives of the victims of an IRA bombing in Enniskillen, County Fermanagh, 25 years ago. She then attended a service of thanksgiving, before meeting around 100 people at St Michael's Catholic Church in the town - believed to be the first time the Queen has visited a Catholic church in Ireland.