Ulvaeus, who along with Benny Andersson wrote songs like "Dancing Queen" and "Waterloo", told the Sunday Telegraph he wanted fans to remember the band as "young, exuberent, full of energy and ambition".
"We will never appear on stage again," he said. "There is simply no motivation to regroup. Money is not a factor and we would like people to remember us as we were."
He added: "I remember Robert Plant saying Led Zeppelin were a cover band now because they cover all their own stuff. I think that hit the nail on the head."
In a joint interview with Andersson, Ulvaeus also paid tribute to Meryl Streep, the star of the "Mamma Mia!" film, describing her as a "goddess".
All four former members of ABBA appeared together in public at the film's Swedish premiere Friday for what is thought to be the first time since 1986.