The Obamas greeted the Trumps at the grand North Portico, the column-lined entrance facing Pennsylvania Avenue.
Mr Obama told Mr Trump it was good to see him and they exchanged pleasantries.
Moments before, Mr Obama was filmed appearing to leave a letter in the Oval Office for his successor to pick up before he walked out for the last time.
A relaxed Mr Obama also found time to crack a joke, switching the order of the four as they posed for pictures while saying: "Now we can take the picture, I'm always on the left."
Mr Obama leaves power hours after making history by cutting short the sentences of 330 federal inmates convicted of drug crimes, the highest total for a single day in history.
It brings his total for the entire eight-year tenure to 1,715, which again stands at more than any other president in US history.
“He wanted to do it. He wanted the opportunity to look at as many as he could to provide relief,” Neil Eggleston, Mr Obama's White House counsel, said in an interview in his West Wing office.
“He saw the injustice of the sentences that were imposed in many situations, and he has a strong view that people deserve a second chance.”
Protests against Mr Trump's presidency meanwhile suddenly turned violent just a few hundred metres from The Mall.
Groups dressed in black and balaclavas can be seen rushing away from Capitol Hill after some clashes with police.
Shortly before Senator Roy Blunt's opening remarks as inaugural committee chairman, police could be seen firing what is believed to be pepper spray and at least one protestor could be seen smashing a glass window.
One person can be seen running up to a glass shop window with a hammer.
BuzzFeed News reporter Zoe Tillman, who was amid the protests on 12th Street, described heavy pepper spray and "police pushing everyone".
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