Giuliani 'to follow'
Reacting to the news, Obama praised Edwards on Wednesday for spending a "lifetime fighting to give voice to the voiceless and hope to the struggling, even when it wasn't popular to do".
Clinton told NBC that it was crucial to remember the "very important" contribution Edwards made "to encourage us to focus on poverty".
Edwards did not indicate whether he would endorse either Obama or Clinton for the nomination.
Such a seal of approval could boost either one's campaign.
Meanwhile it is widely expected that Rudy Giuliani, the former New York mayor, will drop out of the Republican presidential race on Wednesday evening.
Giuliani finished a distant third in the Florida primary on Tuesday, behind winner John McCain and Mitt Romney.
He had once been considered the Republican frontrunner, but a risky strategy of gambling much of his campaign success on winning Florida backfired after McCain, the Arizona senator, surged in polls.
Sources within the Republican party said Giuliani would announce he is to endorse McCain after leaving the campaign.
The Republican presidential candidates are due to take part in the latest presidential debate at the Ronald Reagan Presidential Library in Simi Valley, California, on Wednesday night.
Edwards made the decision to run for the nomination despite his wife's cancer recurring last year.
A former trial lawyer, Edwards launched his campaign in New Orleans last year, calling for action on US poverty.
He ran for the Democratic presidential nomination in 2004 and after losing was picked by John Kerry as his prospective vice-president in that year's White House race which Kerry lost to George Bush.