The museum will present memoribilia from the quartet, including clothing worn by the band, instruments and song lyrics written by Abba.
Abba finished their musical career in 1982. "It is nice someone feels compelled to take on our musical history," the group said in a statement.
The museum has been in the planning stages for two years, and spent that time trying to convice band members to collaborate on the project.
Stockholm believes that they will attract 500,000 people each year to visit the museum. Abba still sells than 3 million discs each year.