The former US president will say his Republican successor "hasn't grown into the job because he can't".
At the White House, Mr Trump hit back that he was only elected because of the "horror" Mr Obama left Americans.
On the third night of the Democratic conference, Kamala Harris will accept the vice-presidential nomination.
The Democratic presidential nominee, Joe Biden, will cap off the four-night convention with a speech on Thursday.
The Biden-Harris ticket will challenge President Trump and his Vice-President Mike Pence for the White House in the election on 3 November.
What will Obama say?
On Wednesday night, Mr Obama will unleash possibly his most scathing attack yet about Mr Trump, speaking from the Museum of the American Revolution in Philadelphia.
According to pre-released excerpts of his remarks, he will say: "He's [Mr Trump] shown no interest in putting in the work. No interest in finding common ground.
"No interest in using the awesome power of his office to help anyone but himself and his friends.
"No interest in treating the presidency as anything but one more reality show that he can use to get the attention he craves."
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He will say the consequences of the Trump presidency have been "our worst impulses unleashed, our proud reputation around the world badly diminished, and our democratic institutions threatened like never before".
Mr Obama will then pivot to encouraging voters to elect his former vice-president, Mr Biden - praising him as "my friend" and "a brother" - in 76 days' time.
Former US presidents mostly tend to observe a dignified public silence about their successors.
But Mr Obama warned four years ago while still in office that he would regard it as a "personal insult" if Americans elected Mr Trump, then the Republican candidate and a former star of TV's The Apprentice.
The 44th president has become gradually more outspoken about his successor as he has watched him dismantle his legacy.
How did Trump respond?
During a White House news conference on Wednesday, Mr Trump was asked about his predecessor's remarks.
"I see the horror that he's left us and the stupidity of the transactions he made," the US president said.
"Look at how bad he was how ineffective a president he was, he was so ineffective, so terrible."
"Now President Obama did not do a good job, and the reason I'm here is because of President Obama and Joe Biden."
He added: "They did such a bad job that I stand before you as president."
Who else is speaking at the convention?
In a pre-recorded speech on Wednesday night, Hillary Clinton, the 2016 Democratic nominee, will also assail the man who thwarted her White House ambitions.
According to excerpts from her prepared remarks, she will say: "I wish Donald Trump had been a better president. But, sadly, he is who he is."
She will add: "For four years, people have said to me, 'I didn't realise how dangerous he was.' 'I wish I could go back and do it over.' Or worst, 'I should have voted.'
"Well, this can't be another woulda coulda shoulda election."
The former first lady and ex-secretary of state will urge Americans: "No matter what, vote. Vote like our lives and livelihoods are on the line, because they are."
Obama's legacy on the ballot
Barack Obama and Donald Trump are exchanging barbs in near real time now. While the former president has offered oblique criticism in the past, in his Democratic National Convention speech tonight he will attack the current president by name.
For more than three years, Trump has treated the 2016 election - one he narrowly won - as a full-throated repudiation of his predecessor and governed accordingly. That has been a risky assumption, given that polls indicate Mr Obama is currently one of the most popular political figures in the nation, while Mr Trump has been net negative for most of his presidency.
Wednesday's clash suggests that the forthcoming election between Mr Trump and Joe Biden, Americans will be more than a choice between two men, it also will be one between two legacies - Mr Obama's and Mr Trump's.
And both the current and former presidents are treating it accordingly.
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