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The two are set to start campaigning together soon.
"I want those of you who've been with me from the beginning of this incredible journey to be the first to know that 'I'm with Her.' I am fired up and cannot wait to get out there and campaign for Hillary," Mr Obama said in the video.
"Secretary Clinton and Senator Sanders may have been rivals during this primary, but they're both patriots who love this country and they share a vision for the America that we all believe in."
The two ran against one another for the Democratic nomination in 2008 and Mr Obama later made Mrs Clinton secretary of state.
Speaking to Reuters following the endorsement, Mrs Clinton said Mr Obama's endorsement "means the world".
"It is absolutely a joy and an honour that President Obama and I, over the years, have gone from fierce competitors to true friends," she said.
Analysis - Anthony Zurcher, BBC News North America reporter
Barack Obama is now in the game. In a slickly produced video endorsement, the president has thrown his support behind Hillary Clinton's bid to keep the White House in Democratic hands.
Given the high production value of the video, the announcement had obviously been in the works for some time. In fact, astute observers have noted that Mr Obama is sporting the tie he wore on Tuesday.
Bernie Sanders has said he will continue to campaign in Washington DC, leading up to the capital city's primary next week - but expect most Democrats to close ranks quickly. The Vermont senator even struck a more conciliatory tone after a meeting at the White House, saying he looks forward to "working together" with the former secretary of state to defeat Donald Trump.
Mr Obama and Mrs Clinton will make their first joint appearance together in Wisconsin next week. Before that she's visiting Ohio and Pennsylvania.
The Democrats clearly view the general election battleground as the industrial Rust Belt states. And for the first time since 1998 there is a popular, scandal-free second-term incumbent president working hard on the campaign trail to preserve his legacy.