The film, which was directed by Lana Wilson, will debut on the streaming service on 31 January, after making its official debut at this year's Sundance Film Festival on 23 January.
The news comes after it seemed uncertain whether the documentary would be released at all, after Swift became caught up in a feud with music manager Scooter Braun.
Braun, who manages artists including Justin Bieber, acquired the copyright to Swift's first six albums after buying her former record label, Big Machine Records.
He declined to license the music for use in the film – Swift also claimed he would only let her use her music if she agreed to stop talking about him in public.
Last month, Variety reported that the music rights had been cleared "in a timely manner".