“There has never been a man or woman, not me, not Bill, nobody more qualified than Hillary” to be president, he said.
When boos rang out at the name of the Republican candidate, Mr Obama simply said: “Don’t boo. Vote.”
Mr Trump responded by rejecting the president’s portrayal of optimism.
“Our country does not feel ‘great already’ to the millions of wonderful people living in poverty, violence and despair,” he said on Twitter.
Mr Obama extolled Mrs Clinton’s character, calling her a “leader with real plans to break down barriers, blast through glass ceilings and widen the circle of opportunity to every single American”.
“She’s been there for us, even if we haven’t always noticed,” he said.
Mr Obama described his nation as “full of courage”, “decent and generous”, but also concerned about racial divisions and “frustrated with political gridlock”.
He said: “Tonight, I ask you to do for Hillary Clinton what you did for me. I ask you to carry her the same way you carried me.”
President Obama is good at this. He’s really, really good at this.
For all his flaws – and conservatives will be quick to point them out – he’s always been able to deliver a pitch-perfect speech on the biggest stages, and this was no exception.
It was the kind of speech that had some conservatives shaking their heads, wondering how their party ceded the optimistic high ground to their opponents. Mr Obama even quoted Ronald Reagan’s “shining city on a hill” line, if only to make the political shift all the more clear.
But he also reserved fierce words for Mr Trump, challenging the Republican’s view of the US as “a divided crime scene”.
Mr Obama said the US he knew was not a “country where we turn against each other, and turn away from the rest of the world”.
He added: “Our power doesn’t come from some self-declared saviour promising that he alone can restore order as long as we do things his way.”
Turning to Mr Trump’s business acumen, he said: “I know plenty of businessmen and women who have achieved remarkable success without leaving a trail of lawsuits and unpaid workers and people feeling like they got cheated.”
Mr Obama added: “Does anyone really believe that a guy who spent his 70 years on this Earth showing no regard for working people is suddenly going to be your champion, your voice? No.”
The former secretary of state joined him on stage for a hug after he finished speaking.