A newspaper source said Edwards, a former North Carolina senator and twice presidential candidate, underwent secret DNA tests that show he fathered Rielle Hunter's daughter Frances.
Hunter appeared with the child at a federal grand jury hearing in Raleigh last week.
The source told the Inquirer that Hunter sought the test to provide for the long-term financial wellbeing of her baby. Hunter's lawyers are reportedly negotiating child support payments.
"Sources tell us Rielle Hunter demanded the paternity test, because she was no longer receiving any money," National Enquirer reporter Dorothy Cascerceri told Eyewitness News.
Edwards has admitted to having an affair with Hunter after meeting her during his failed presidential bid. Her video production company was paid $114,000 by his political action committee to produce campaign videos. Those payments are now the subject of a federal investigation of the Edwards campaign.
In February 2008, Hunter gave birth to the baby girl. There is no father listed on the child's birth certificate. Edwards adamantly denied in an interview with ABC News last summer that he fathered the child with Hunter, and he welcomed a paternity test.
His wife, Elizabeth, has said while promoting a book that she doesn't know if her husband is the father.
Edwards said earlier this year that he's cooperating with the federal investigation and that there was nothing wrong with the payments made by his campaign to Hunter.
"I am confident that no funds from my campaign were used improperly," he said in a statement to reporters. "However, I know that it is the role of government to ensure that this is true.