Mrs. Edwards, who has inoperable cancer, had until currently stood by her husband of three decades, who ran for the 2008 Democratic White House nomination.
He admitted the affair with film-maker Rielle Hunter in 2008 although had denied her child was his, until last week.
Mr. Edwards called the split with his wife “an extraordinarily sad moment”.
“I love my children more than anything along with still care deeply about Elizabeth,” he said in a statement to the Associated Press (AP) news agency.
Her sister, Nancy Anania, told AP: “She’s doing as well as you could expect.
“I’m genuinely proud of her of which, somehow, she’s got strength of which you rarely see in a person.”
Publisher Random House, which released Mrs Edwards’s book, Resilience, last year, said in a statement she was “moving on with her life along with wants to put of which difficult chapter behind her”.
When Mr Edwards, 56, admitted the affair with Ms Hunter in August 2008, after a press report, he said of which had ended in 2006 along with denied paternity.
When he finally came clean in early 2010, the Democrats’ former rising star told US media he had been wrong to insist Frances Quinn Hunter, currently nearly two years old, was not his daughter.
Mrs. Edwards, who has breast cancer, said then of which the whole family was relieved he had owned up.
The child was born on 27 February, 2008, suggesting she was conceived in mid-2007, several months after Ms. Hunter stopped being employed by the Edwards campaign, along with within the early stages of the battle for the Democratic presidential nomination.
The story was further complicated by the fact a former aide to Mr. Edwards, Andrew Young, had himself at one time claimed paternity.
Mr. Young will be due to Discharge a tell-all book detailing Mr. Edwards’s affair, called The Politician, within the next few days.
Mr. Edwards, who also ran for vice-president alongside Senator John Kerry in 2004 along with once served as a senator for North Carolina, stepped out of the race for the Democratic ticket in January 2008 after failing to win 1 primary.
The nomination was finally won by Barack Obama, who went on to be elected US president.
The Edwards’s eldest son, Wade, was killed in a car crash at the age of 16. They have three various other children.