Her 1989 album won the award at this year’s Grammys in Los Angeles.
Kendrick Lamar won the most prizes on the night with five awards.
Taylor Swift also won best pop vocal album and best music video for her track Bad Blood.
Ed Sheeran also won his first two Grammys for song of the year and best pop solo performance for his number one hit Thinking Out Loud.
A surprised Ed Sheeran beat Kendrick Lamar, Taylor Swift, country group Little Big Town and Wiz Khalifa to the song of the year accolade.
Taylor Swift was equally surprised at winning the top honor. Her album, which was released in 2014, came out too late to be eligible for last year’s awards so was finally recognized at this year’s ceremony.
The singer gave a powerful acceptance speech saying: “As the first woman to win album of the year at the Grammys twice, I want to say to young women: There are going to be people along the way who will try to undercut your success or take credit for your accomplishments or your fame.
“But if you focus on your work and don’t let those people sidetrack you, someday when you get where you’re going, you’ll look around and you’ll know it was you and the people that love you that put you there. And that will be the greatest feeling in the world.”
Kendrick Lamar’s wins included best rap album for To Pimp A Butterfly; best rap song and rap performance for Alright; best rap/sung collaboration and best music video, which he shared with Taylor Swift for Bad Blood.
Alabama Shakes were triple winners. They collected best alternative music album while their song Don’t Wanna Fight won best rock song and rock performance.
The Weeknd also picked up two Grammys for best urban contemporary album and best R&B performance.
Mark Ronson and Bruno Mars won two awards for their hit Uptown Funk, including record of the year, while Meghan Trainor was named best new artist.
Muse also won best rock album for Drones, and Tony Bennett collected his 18th Grammy for best traditional pop vocal album.
Justin Bieber also won his first Grammy for his collaboration with Skrillex and Diplo, winning best dance recording for Where Are U Now.
Amy – Asif Kapadia’s documentary on the life of Amy Winehouse – won the Grammy for best music film.
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