"Thank-you so much. We're thrilled to be here," the President replied
And despite the grey skies, he remarked optimistically: "The sun's coming out - I can feel it."
He signed the visitor's book before holding private talks in the drawing room of the Aras.
The meeting of President McAleese and her husband Martin, who has just been appointed a Senator by Taoiseach Enda Kenny, with Mr Obama and his wife Michelle, is the first in a busy schedule of events.
The rain let up to allow both couples to take a short walk in the gardens and pose for pictures.
The US President took part in a tree-planting ceremony before schoolchildren rang the Peace Bell unveiled in the grounds of Aras in 2008 by Mrs McAleese to mark the 10th anniversary of the Good Friday Agreement.
The Obamas chatted and posed for photographs with the youngsters before leaving for talks with the Taoiseach.
The ceremony to plant the Irish oak took place about 50ft from a sequoia planted in 1963 by President John F Kennedy
After the Aras visit, Mr Obama was met at the state residence, Farmleigh, by Taoiseach Enda Kenny, and his wife, Fionnuala.
The President, the Taoiseach and Tanaiste then held talks in the drawing room which officials said would cover "all matters of a national interest".
It is understood one of the Taoiseach's aides arrived at Farmleigh ahead of the meeting carrying a hurley – believed to be a gift for the President.
Air Force One landed amid tight security and wet, blustery conditions at Dublin Airport just after 9.30am.
After the Aras an Uachtarain visit, Mr Obama will meet Mr Kenny for 45 minutes of talks.
The President will then travel to his ancestral home in Moneygall, Co Offaly, ahead of a public concert later in Dublin.
Mr Obama waved as he stepped off the plane with his wife, Michelle.
The visit lacked the ceremony of last week's state visit of the Queen, with only a small welcoming party waiting on the runway apron to greet the President and shake hands.
Airspace around Dublin was been shut down for the President's arrival and transfer over the capital.