The museum, a permanent exhibition within a hall of fame of Swedish pop music, opens in May next year. It will feature memorabilia like stage costumes worn by the singers, and visitors will also be able to sing along to ABBA songs alongside life size holograms of the group.
But while Ulvaeus -- now a 67-year-old grandfather - is involved in setting up the museum, there will be no new performances from a group that last appeared on stage around 30 years ago.
"For the opening of the museum I cannot say. I will have to give everyone (each group member) a preview and take it from there," Ulvaeus told Reuters in an interview.
"There will never be a musical reunion ... oh, I should say on stage, never a musical reunion," he added, laughing and refusing to give more details. "It means on stage nothing would happen."
ABBA, made up of Agnetha Faltskog, Anna-Frid Lyngstad, Benny Andersson and Bjorn Ulvaeus, shot to fame when they won the 1974 Eurovision Song Contest with the song "Waterloo".
They went on to become one of Sweden's biggest exports with such hit songs as "Dancing Queen" and "Gimme Gimme Gimme (A Man After Midnight)".
But the museum took a long time coming. Separate plans for an earlier museum on ABBA were shelved in 2008.
"We weren't entirely sure if there was going to be one, whether we wanted one, becoming artifacts and relics while we are still alive," Ulvaeus said.
"It is such a long time ago that ABBA was active .. the guy I see when I look at all the videos, on stage, it is almost that he is a stranger," Ulvaeus added.
"It is almost that I didn't know him anymore. I thought it would be interesting to get to know him a little better."
Ulvaeus said that Catherine Johnson, who wrote the musical "Mamma Mia!", was helping write the audio guide which would feature the band's members telling visitors about the exhibits.
The group sold around 370 million records in total and are part of a rich Swedish pop tradition which includes Roxette, Ace of Base, Europe and Kent.
After ABBA, Ulvaeus went on to become a successful businessman and helped to produce the hugely successful "Mamma Mia!" musical that was later turned into a film.
He is still in contact with the members of the group, and is working with Benny Andersson on a musical drama at a theatre in Stockholm in February.
"When I look at old videos and photos it is almost always with great pride because we took the music so seriously," he said. "You can hear that and I think that is why it is still around today.
"The outfits and all that, we were having fun," he said. "There was nothing serious about that - but the music, yes."
Ulvaeus says the prime motivation for the museum is being able to show his grandchildren what ABBA was about.
"The reason I am in this at all is that I am in Stockholm. This is where I will go past with my grandchildren and they will ask me what is in there, granddad," he said.
"And I want to be proud of what is in there."
(Editing by Paul Casciato)
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