The 'Top Gun' and 'ER' star, who met Goddard when he was 12, opened up in an emotional essay he shared on the Medium website, titled 'Yes Mom, There Is Something Wrong'.
Edwards, 55, says he was 14 years old when "my mother opened the door for me to answer honestly about the rumors she had heard about Gary Goddard — who was my mentor, teacher and friend — being a pedophile.
"I was molested by Goddard, my best friend was raped by him — and this went on for years. The group of us, the gang, stayed quiet."
Explaining why he could never speak up, Edwards continues: "One of the most tragic effects of sexual abuse in children is that the victims often feel deeply responsible — as if it is somehow their fault.
"With their sick form of control, abusers exploit a child's natural desire to bond. The victims are required to play by the abuser's rules, or else they are "out" — banished from the only world they know."
The actor also reveals that he confronted Goddard at an airport 22 years ago, and that he "swore to his remorse and said that he had gotten help."
On Friday, Goddard's spokesperson Sam Singer issued a statement denying the allegations, saying: "As to the allegations that Mr. Edwards made in his post today, I can unequivocally deny them on Gary's behalf.
"Gary first met Anthony more than 40 years ago. Gary was a mentor, teacher and a friend to Anthony, which makes this story all the more disturbing to him."
He continued: "Gary played an important role in helping start Anthony's acting career and acted as his personal manager. He has nothing but the greatest respect for Anthony as a person. Gary is saddened by the false allegations."
The allegations are the latest in a mounting wave of sexual misconduct accusations levelled against some of Hollywood's biggest players.