Mr Edwards, a former Democratic senator from North Carolina and 2004 vice-presidential candidate, had initially denied having the child with videographer Rielle Hunter, who worked for him in the early stages of the battle for the 2008 Democratic presidential nomination.
But as the second birthday of Frances Quinn Hunter approaches, he admitted: "I am Quinn's father." He vowed to do "everything in my power" to support her. "It was wrong for me ever to deny she was my daughter and hopefully one day, when she understands, she will forgive me," he said.
A former Edwards aide, Andrew Young, initially claimed paternity of the child. Mr Young is scheduled to release a book next month that details the scandal.
Mr Edwards' wife of more than 30 years, Elizabeth, has been battling incurable cancer since March 2007. She has stood by her husband despite the affair.