President-elect Obama and President Bush met in the Oval Office, their first substantive one-on-one session, while first lady Laura Bush and Obama's wife, Michelle, talked in the White House residence.
The president later escorted his successor to his limousine. Obama's wife was leaving separately after her discussions with Laura Bush.
None of the four spoke to reporters.
It was Obama's first visit to the Oval Office. The agenda was kept private, although he and Bush were expected to discuss their transition of power and such pressing issues as the war in Iraq and the country's economic downturn.
The Obamas arrived at the South Portico 11 minutes early with Bush and the first lady waiting for them. Mrs. Bush and Mrs. Obama greeted each other warmly while the president and his successor exchanged smiles and a handshake.
Taking a bit of prerogative, the president-elect put his left hand on Bush's back as the two couples entered the Diplomatic Reception Room.
Bush and Obama then strolled along the Colonnade and waved for the cameras.
The president-elect's arrival had the look of a head-of-state state visit, although there were no fife and drum bands, speeches or official pageantry.
Changes from candidate to president-elect were evident earlier, when Obama stepped off his plane and was greeted by transition manager John Podesta, the former chief of staff to President Clinton.
Obama climbed into a black limousine with tinted windows, instead of his normal SUV; the limo looked just like the one that the president rides in, without the seal or flags. The entire motorcade was upgraded from campaign mode to presidential-level, with an identical decoy limousine, a black haz-mat truck, a communications truck and the counter-assault team hanging out the back of an SUV.
Mrs. Bush was to give Mrs. Obama a tour of the first family's living quarters, including the bedrooms used by children of past presidents. White House press secretary Dana Perino said the two women were expected to talk about living in one of the world's most famous buildings, from family life to the help provided by executive staff.
The Obamas have two daughters: Malia, 10, and Sasha, 7. Obama started his day in Chicago, dropping the two girls at school, each with a kiss, and then going to a gym for a workout.
Obama told reporters last week that he was headed to the White House meeting with "a spirit of bipartisanship."
He ran a campaign in which he relentlessly linked Republican opponent John McCain to Bush and presented his ideas as a fresh alternative to what he called Bush's failed policies. Yet the tone changed almost immediately after Obama's win last Tuesday.
Bush, who had endorsed McCain, lauded Obama's victory as a "triumph of the American story." He warmly invited the Obama family to the White House.
Obama, in turn, thanked Bush for being gracious. The president-elect has made clear in public that there is only one president and for now that's Bush. Obama takes the oath of office on Jan. 20.
Josh Bolten, Bush's chief of staff, said Bush and Obama probably each had a list of issues to discuss.
"I know the president will want to convey to President-elect Obama his sense of how to deal with some of the most important issues of the day," said Bolten, interviewed on C-SPAN by reporters from The Associated Press and The Washington Post. "But exactly how he does that, I don't know, and I don't think anybody will know."
Unlike the incoming president, Bush knew his way around the Oval Office by the time he was elected in 2000 - his father had been president. Still, like many before them, President Clinton and President-elect Bush had their own private meeting, keeping up a tradition that temporarily puts the presidency above politics.
Obama has been to the White House before, including an emergency leadership session to deal with the financial crisis in September.
But an Obama spokeswoman said the president-elect had never been in the Oval Office.
(Copyright 2008 by The Associated Press. All Rights Reserved.)