Williams was the first black woman to be named Miss America in 1983 but resigned after a magazine published nude photos of her without her consent.
"I want to apologise for anything that was said or done," said Miss America CEO Sam Haskell.
A tearful Williams called the statement "unexpected" and "beautiful".
Now 52, she has forged a career as an actress, with major roles in Ugly Betty and Desperate Housewives.
She also scored a global hit in 1992 with the ballad Save the Best for Last; and her recording of Colors of the Wind from Disney's Pocahontas soundtrack earned her a Golden Globe, a Grammy and an Oscar for best original song.
The New Yorker won Miss America in September 1983 but, months later, the pageant's executive committee voted unanimously to request that she resign after Penthouse magazine published naked photographs she had posed for several years earlier,
Williams remains the only title-holder who was asked to resign in the pageant's history.
She was invited back to the competition this year by Chairman Sam Haskell, who asked her to serve as head judge.
Before the competition started, he invited her on stage to receive the apology.
"I have been a close friend to this beautiful and talented lady for 32 years," he told the audience. "You have lived your life in grace and dignity, and never was it more evident than during the events of 1984 when you resigned.
"Though none of us currently in the organization were involved then, on behalf of today's organization, I want to apologize to you and to your mother, Miss Helen Williams."
He continued: "I want to apologize for anything that was said or done that made you feel any less than the Miss America you are and the Miss America you always will be."
The audience gave Williams a standing ovation and TV coverage showed her mother on the verge of tears.
"Thank you so much, Sam, so unexpected but so beautiful," said the actress.
"I did the best that I could as Miss America in 1983 to 84," she said.
"On behalf of my family, my mother in particular; [publicist] Brian Edwards, who orchestrated this entire thing to bring me back; and your leadership, your integrity and you bringing this pageant back to what it ought to be. I love you. I love the girls. And I'm so honoured to be back."
Williams then returned to her seat and helped select the new Miss America - 21-year-old Betty Cantrell of Georgia.
Organisers of the Miss America pageant have apologised to actress Vanessa Williams, 32 years after she was forced to hand back her title.