Accompanied by Gordon Brown, the British prime minister, Bush will also meet Brian Cowen, the Irish premier, and Ian Paisley, the former Northern Irish first minister.
He is expected to be briefed on the results of a recent Belfast conference that aimed to attract US investment to the province.
The president will on Monday also visit an integrated Catholic/Protestant primary school during the brief stopover.
Upon arriving, he travelled immediately to Stormont, the seat of devolved government, which restarted last year in Northern Ireland, after three decades of civil unrest known as the Troubles before accepting the 1998 Good Friday peace agreement.
The DUP's Robinson took over from Paisley this month after fears that Sinn Fein, its power-sharing partners and former foes, could scupper his appointment proved unfounded.
Mixed welcome
Some see Bush's visit as a welcome vote of confidence in Northern Ireland, while others have used the opportunity to protest against the Iraq war and on human rights issues.
Several hundred people holding placards such as 'Bush Not Welcome: Shame On The Assembly' and 'Bush Out' gathered in central Belfast ahead of the visit to protest the Iraq war, including a large group from Sinn Fein.
"We don't have money for fixing roads, for bread and butter issues but we're prepared to splash out millions on making this guy feel welcome," Stephen Mulligan, a Sinn Fein worker said.
Later, around 70 people staged a noisy protest outside the main gates of Stormont as Bush arrived, although his motorcade did not pass directly by.
Riot police looked on as demonstrators shouted slogans and gave speeches.
Amnesty International, the human rights group, held a protest on Sunday and has written to Robinson and McGuinness asking them to raise issues such as the US military camp at Guantanamo Bay with Bush.
Sign of stability
While some may be concerned over Bush's record on human rights, others welcomed his visit as a sign of stability in Northern Ireland.
In an editorial on Monday, the News Letter newspaper described as "remarkable" Bush's trip, his second as president.
"That he has done so is a strong vote of confidence in the province and the transformation that has taken place," it said.
"We should seize the opportunity to showcase our country."
The Belfast Telegraph simply headlined its piece on the visit: 'Bush Backs Us'.