The 30-year-old Swede, who currently plays for Wigan, believed he was entitled to a portion of his transfer fee and was granted the money by a court after the Eredivisie club contested the claim.
However, he discovered two months ago the club had been right and has now given back the money.
Edman, who played for Heerenveen for three years, told the club website: "I was wrong. I was misguided.
"At that time I didn't know what kind of games are played in the football world. I have made a big mistake and I want to make up for that as much as possible."
Edman, however, admitted he has not been able to pay back the full amount.
He continued: "I regret it that things went as they did in the past. Heerenveen have been very important in my career.
"I can't make up for my mistake entirely, because part of that money went to my agent. But my part has been deposited by me to Heerenveen."