President Mary McAleese will represent the Irish people and Taoiseach Bertie Ahern will also be present.
For the first time ever a US president will attend. George W Bush, with whom the Pope disagreed about the Iraqi war, is travelling with his wife Laura.
Polish President Aleksander Kwasnievski and Lech Walesa, the former leader of Solidarity, will also attend.
Britain’s Prince Charles moved his wedding from Friday to Saturday to represent his mother Queen Elizabeth II at the funeral. His fiancee, Camilla Parker Bowles, will not attend.
The body of the late pontiff made its last journey to the spot above where St Peter was buried around 4pm Irish time yesterday.
He will lie here in state until early on Friday morning for the public to pay their last respects. An estimated one million people are expected to file past.
The Basilica will remain open except between 2am and 5am for cleaning, Vatican spokesman Joaquin Navarro-Valls said.
After Requiem Mass on Friday at 10 am, accompanied only by a few clergy and his “family” - his Polish secretary and the nuns who looked after him - the Pope’s body will be brought to the crypt.
There it will be placed in the tomb that once held the coffin of Pope John XXIII, which some years ago was moved into the Basilica.
The details of the Mass are yet to be decided - whether it will be an intensely solemn High Mass or the more simple one requested by the last Pope, John Paul I.
The main celebrant will be Cardinal Joseph Ratzinger, the German some believe could be the next Pope.
There was speculation that the late pontiff would wish to be buried in Krakow in Poland where he was archbishop and that he would want to be buried in a plain pine coffin like his predecessor. However, Mr Navarro-Valls said he had not made such a request.
It was thought the Pope would have made such requests in his will, which was expected to be read by the cardinals when they met yesterday for the first time since the Pope’s death.
However, the 65 cardinals who attended the two-and-a-half-hour meeting spent the time discussing the funeral arrangements and did not read the will, the spokesman said. They took an oath of secrecy at the start of the meeting, promising not to reveal any details of the selection of the next pope.
Bishop John Magee of Cloyne, who was secretary to the late Pope and who flew to Rome on Sunday, spent time in the Salle Clementine, where the body was first laid in state.
Several other members of the Irish hierarchy are expected over the next few days, including Cardinal Desmond Connell, who will be one of the 117 cardinals voting.
Ireland’s second cardinal, Cahal Daly, is not travelling because of illness and, as he is over 80 years of age, he does not have a vote.
The cardinals will meet every day to discuss arrangements and to decide when to hold the conclave to elect the next pontiff.
Between now and then, the cardinals will be mixing piety with a little politicking as they discuss the issues facing the Catholic Church and the kind of person best suited to deal with them.
Security will be very tight for the funeral with more than 6,000 police on duty, while the Italian airforce will enforce a no-fly zone above the city.
An army of volunteers was being organised yesterday to manage the estimated two million pilgrims expected to come to the city, making it the biggest pilgrimage ever to the holy city.
Extra public transport is being laid on and work on the subway has been suspended to re-open lines closed for maintenance.