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 also told NBC that it was important to remember the "very important" contribution Edwards made "to encourage us to focus on poverty".
Meanwhile it is widely expected that Rudy Giuliani, former New York mayor, will drop out of the Republican presidential race.
Giuliani finished a distant third in the Florida primary on Tuesday, behind winner John McCain and Mitt Romney.
Previous campaigns
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.
However Kerry lost the election to George Bush.