Swift, now in the middle the world's highest-grossing concert tour, also announced she would release a new album in April.
The 34-year-old won album of the year for "Midnights," eclipsing music legends Frank Sinatra, Paul Simon and Stevie Wonder, who each claimed the prize three times.
On stage, Swift said she was thrilled by the honor and that she would keep writing and singing songs.
"It makes me so happy," she said. "All I want to do is keep doing this."
Earlier, Swift claimed the prize for best pop vocal performance and used the moment to announce that she will release "The Tortured Poets Department" on April 19.
"I want to say thank you to the fans by telling you a secret that I've been keeping from you for the last two years," Swift said as she disclosed the new album.
Female artists swept the major awards on Sunday.
Billie Eilish claimed song of the year for "What Was I Made For?," a ballad written for the "Barbie" movie soundtrack. Miley Cyrus landed the record of the year for her empowerment anthem "Flowers."
Best new artist went to R&B and pop singer Victoria Monet.
Winners were chosen by the musicians, producers, engineers and others who make up the Recording Academy. The group has worked to diversify its membership in recent years by inviting more women and people of color to its ranks.
