Edwards confirmed this in a statement released to The Associated Press, after initially denying that he'd fathered a child during an affair with campaign aide Rielle Hunter.
"I am Quinn's father," the former senator declared in his statement, as the second birthday of Frances Quinn Hunter approaches.
A former Edwards aide, Andrew Young, initially claimed paternity of the child shortly before the 2008 presidential primary contests began. Young is scheduled to release a book on Feb. 2 that details the scandal.
Frances was born Feb. 27, 2008, indicating that the child was conceived in the middle of 2007, several months after Hunter stopped working for Edwards. John and Elizabeth Edwards renewed their wedding vows in July of 2007 to celebrate their 30th wedding anniversary.
Elizabeth Edwards, whose cancer returned in an incurable form in March 2007, has stood by her husband despite the affair. She has said that it does not matter to her whether her husband fathered a child with Hunter, saying, "that would be a part of John's life, but not a part of mine."
Since admitting the affair in August 2008, John Edwards has largely gone into seclusion. He has acknowledged a federal investigation into his campaign finances while both Young and Hunter -- with her child -- have made appearances at a federal courthouse in Raleigh.
In the statement Edwards released Thursday, he said, "I will do everything in my power to provide her (Frances) with the love and support she deserves. I have been able to spend time with her during the past year and trust that future efforts to show her the love and affection she deserves can be done privately and in peace."
Edwards also said, "It was wrong for me ever to deny she was my daughter and hopefully one day, when she understands, she will forgive me."
"I have been providing financial support for Quinn and have reached an agreement with her mother to continue providing support in the future," the statement said. "To all those I have disappointed and hurt, these words will never be enough, but I am truly sorry."
Harrison Hickman, Edwards' longtime political adviser, called the situation "a lot more complicated than people think."
"There are a lot of adults involved," Hickman said in an interview broadcast on NBC's "Today" show. "I think they wanted to handle this in the right way."
"Elizabeth thinks that he should acknowledge this," Hickman said. He said it "has been a very difficult time for everyone ... but especially for Elizabeth."
Edwards, a U.S. senator representing North Carolina from 1998 until his vice presidential bid in 2004, acknowledged in May that federal investigators were looking into how he used campaign funds. Grand jury proceedings are secret, and the U.S. attorney's office in Raleigh has declined to confirm or deny an investigation.
Edwards adamantly denied during an interview with ABC News last summer that he had fathered a child with Rielle Hunter, and he welcomed a paternity test.
Edwards has said the affair ended in 2006. That year, Edwards' political action committee paid Hunter's video production firm $100,000 for work. Then the committee paid another $14,086 on April 1, 2007. The Edwards camp has said the latter payment from the PAC was exchanged for 100 hours of unused videotape that Rielle Hunter shot.
The same day, the Edwards presidential campaign had injected $14,034.61 into the PAC for a "furniture purchase," according to federal election records.
Fred Baron, who was Edwards' national finance chairman and a wealthy Dallas-based trial attorney, said last year he quietly sent money to Hunter and to resettle Young's family.