The move came after Mr Obama met with her rival, Senator Bernie Sanders.
Mr Sanders said he would work with Mrs Clinton to stop the Republican's presumptive nominee Donald Trump.
In his endorsement, Mr Obama said: "I don't think there's ever been someone so qualified to hold this office."
Mr Obama praised his former secretary of state's experience and grit, and urged Democrats to unite behind her in the fight against the Republicans in the autumn.
"Look, I know how hard this job can be. That's why I know Hillary will be so good at it," Mr Obama said in a web video circulated by the Clinton campaign. "I have seen her judgment. I have seen her toughness."
Mr Obama called for unity among Democrats and vowed to be an active force on the campaign trail.
As the video circulated, Mrs Clinton's campaign announced their first joint appearance on the campaign trail will be on Wednesday in Green Bay, Wisconsin. The campaign said Mr Obama and Mrs Clinton will discuss building on the progress made during his presidency "and their vision for an America that is stronger together".
Mr Obama's endorsement came as the Democratic establishment piled pressure on Mrs Clinton's primary rival, Mr Sanders, to step aside so Democrats could focus on defeating Mr Trump.
Mr Sanders emerged from his meeting with Mr Obama and inched closer in that direction. Although he stopped short of endorsing Mrs Clinton, the Vermont senator told reporters he planned to press for his agenda at the party's July convention and would work with Mrs Clinton to defeat Mr Trump.
"Needless to say, I am going to do everything in my power and I will work as hard as I can to make sure that Donald Trump does not become president of the United States," he said.
Mr Sanders, standing in the White House driveway with his wife, Jane, at his side, said he would compete in the Washington DC primary on Tuesday, the party's final contest, but noted his interest was largely in pushing for statehood.
Mr Sanders' remarks came after a longer-than-expected Oval Office meeting with Mr Obama, part of Democratic leaders intensifying effort to unite behind Mrs Clinton as the nominee of the party.
Mrs Clinton declared victory over Mr Sanders on Tuesday, having captured the number of delegates needed to become the first female nominee from a major party.
Though Mr Sanders has shown signs he understands the end of his race is near - he was about to let go off about half of his team - he has vowed to keep fighting, stoking concern among party leaders eager for the primary race to conclude.
Mr Sanders is planning a rally on Thursday evening in Washington, which holds the final primary contest next week.
As he met with leaders on Capital Hill, Mr Sanders ignored a reporter's question about the president's endorsement.
The situation has put Mr Obama, the outgoing leader of his party, in the sensitive position of having to smooth relations between Mrs Clinton and Mr Sanders without alienating the runner-up's supporters, many of whom are angry over what they see as the Democratic establishment's efforts to force him out of the race. Mrs Clinton is counting on Mr Sanders' supporters backing her to defeat Mr Trump.
Mr Obama has been trying to give Mr Sanders the courtesy of exiting the race on his own terms.
"It was a healthy thing for the Democratic Party to have a contested primary. I thought that Bernie Sanders brought enormous energy and new ideas," Mr Obama said on Wednesday. "And he pushed the party and challenged them. I thought it made Hillary a better candidate."
Mr Obama had planned to use the meeting, which the White House emphasised was requested by Mr Sanders, to discuss how to build on the enthusiasm he has brought to the primary, the White House said.
Mr Sanders also was heading to a meeting with Senate minority leader Harry Reid, who endorsed Mrs Clinton weeks ago. The Vermont senator was also due to meet with vice President Joe Biden.
Even some of Mr Sanders' staunchest supporters have started looking to Mrs Clinton. Senator Jeff Merkley of Oregon, the one Senate Democrat to endorse Mr Sanders, said Mrs Clinton was the nominee and offered his congratulations.
Now head-to-head in the presidential race, Mrs Clinton and Mr Trump are both working to woo Mr Sanders' supporters.
Mr Trump has said he welcomes Mr Sanders' voters "with open arms" while Mrs Clinton has vowed to reach out to voters who backed her opponent in the Democratic primary.
Mr Trump, despite a string of victories this week that reaffirmed his place as the Republican nominee, is still working to convince wary Republicans that he is presidential material. Looking ahead to an upcoming speech attacking Mrs Clinton and her husband, Mr Trump tried to put a row over his comments about a Hispanic judge's ethnicity behind him.
That controversy and others before it have led prominent Republicans, including House Speaker Paul Ryan, to openly chastise their party's nominee.
Yet Mr Trump now has 1,542 delegates, including the 1,447 required by party rules to vote for him at the convention. It takes just 1,237 delegates to win the Republican nomination.
Mr Obama's aides have said he is eager to get off the sidelines and take on Mr Trump. The key question is whether voters who helped elect him twice will follow his lead now that he is not on the ballot. Democrats have yet to see that powerful coalition of minorities, young people and women reliably show up for candidates not named Obama.
"It's going to be hard to get African-American turnout as high as Obama got it, and to get youth turnout as high as Obama got it," said Celinda Lake, a Democratic pollster. "We have to work really hard."