Rajapaksa called the election two years ahead of schedule in an effort to capitalise on the popularity of the military's victory over the Liberation Tigers of Tamil Eelam (LTTE) in May.
Fonseka led the army to victory against the LTTE but later quit, accusing the president of sidelining him due to unfounded coup fears.
"I have never lost a battle. I can win this one too," Fonseka told reporters on Friday, ahead of his formal announcement.
"I am definitely coming forward to defeat the president."
Al Jazeera's Minelle Fernandez, reporting from the capital, Colombo, said Fonseka is confident that he can present a real challenge.
"The general said he has taken on and delivered with every single promise he has made - the campaign, the military victory. Basically he cited those as evidence of him keeping his promises," she said.
But she said Fonseka did not divulge many details about his actual policies or how he would differ from Rajapaksa.
"General Fonseka gave us an overview of what his campaign was comprised of. He said he would look at preserving and consolidating democracy in this country. He said that it is time to ensure that the peace is taken forward, and it is consolidated.
"He did promise that more details would be heard in the coming weeks."
The United National Party (UNP) and 14 other opposition parties have already said that they would back Fonseka as their candidate.
Some analysts have said that Fonseka could split Rajapaksa's support base and unify opposition groups.
"General Fonseka has caused a lot of apprehension in the government and has become a serious challenger," Jehan Perera, an analyst with the non-partisan National Peace Council, said.
Rajapaksa has completed only four years of his six-year term, which ends on November 2011.
The government has attempted to dampen down Fonseka's perceived role in the victory over the LTTE.
The LTTE had been fighting for a separate ethnic-minority Tamil homeland in the northeast. The conflict left more than 80,000 people dead.