Edwards also denied he was the father of Hunter's baby girl, Frances Quinn, although the one-time Democratic Presidential candidate said he has not taken a paternity test.
Edwards said he knew he was not the father based on timing of the baby's birth on February 27, 2008. He said his affair ended too soon for him to have been the father.
A former campaign aide, Andrew Young, has said he was the father of the child.
In his statement, he said, "It is inadequate to say to the people who believed in me that I am sorry, as it is inadequate to say to the people who love me that I am sorry.
"In the course of several campaigns, I started to believe that I was special and became increasingly egocentric and narcissistic. If you want to beat me up feel free. You cannot beat me up more than I have already beaten up myself. I have been stripped bare and will now work with everything I have to help my family and others who need my help."
The National Enquirer first reported on the affair in October 2007, and Edwards denied it.
"The story is false," he told reporters. "It's completely untrue, ridiculous." He professed his love for his wife, Elizabeth, who had an incurable form of cancer, saying, "I've been in love with the same woman for 30-plus years and as anybody who's been around us knows, she's an extraordinary human being, warm, loving, beautiful, sexy and as good a person as I have ever known. So the story's just false."
Last month, the Enquirer carried another story stating that its reporters had accosted Edwards in a Los Angeles hotel where he had met with Hunter after her child's birth. Edwards called it "tabloid trash," but he generally avoided reporters' inquiries, as did his former top aides.
Edwards was a top contender for the Democratic nomination for president. He placed second in the Iowa caucuses last January but dropped out of the race a few weeks later.
Edwards, a former senator from North Carolina, was the Democratic nominee for vice president in 2004.
The Edwardses have three children - Cate, Jack and Emma Claire. Another son, Wade, died at age 16 in a 1996 car accident.
In a statement released Friday night, Elizabeth Edwards said it wasn't easy to find out about her husband John's extramarital affair in 2006 but after a what she called a "long and painful process," his family is supporting him.
Edwards calls her husband's affair was a "terrible mistake." But she says the healing process was "oddly made somewhat easier" after her diagnosis of breast cancer in March 2007.
She said she was proud of the courage her husband showed despite his shame.
She says her family has been through a lot and pleaded for privacy.
David Bonior, Edwards' campaign manager for his 2008 presidential bid, was not as forgiving. He said Friday he was disappointed and angry after hearing about Edwards' confession.
"Thousands of friends of the senators and his supporters have put their faith and confidence in him and he's let them down," said Bonior, a former congressman from Michigan. "They've been betrayed by his action."
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