Swift also announced from the Grammys stage that 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.
Swift said she was thrilled by the honour and gushed about the fulfilment she feels from 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, which was made available for pre-sales during the Grammys telecast.
Swift, who is about to jet to Tokyo to resume the world's highest-grossing concert tour, was among the women who swept the major Grammy awards on Sunday.
Billie Eilish claimed song of the year for "What Was I Made For?," a ballad written for the "Barbie" movie soundtrack.
"As a woman, it feels a lot of the time like you're not being seen," Eilish told reporters backstage. "I feel that this makes me feel very seen. Sometimes it feels really good to have somebody tell you 'good job.'"
Miley Cyrus, winner of her first two Grammys on Sunday, landed the record of the year honour for her empowerment anthem "Flowers."
"This award is amazing," Cyrus said, "but I really hope that it doesn’t change anything because my life was beautiful yesterday."
Best new artist went to R&B and pop singer Victoria Monet, who thanked her mom, "a single mom raising this really bad girl."
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.
SZA, who went into the night as the most-nominated artist, won three trophies including best R&B song for "Snooze."
"I came really, really far," she said. "I can't believe this is happening, and it feels very fake."
Indie rock band boygenius, a band formed by musicians Phoebe Bridgers, Lucy Dacus and Julien Baker, also claimed three awards.
JONI MITCHELL, BILLY JOEL PERFORM
Comedian Trevor Noah, back for a fourth stint as host, opened the show on CBS PARA.O by joking that it was "the only concert that starts on time."
Folk singer Joni Mitchell performed for the first time at the Grammys, singing "Both Sides Now" from a chair and sporting blonde braids and a beret, with Brandi Carlile playing guitar beside her.
In a tribute to the many musicians and industry executives who passed away in the last year, Stevie Wonder played "For Once In My Life" to honour the late Tony Bennett who sang along from a video.
Annie Lennox sang "Nothing Compares 2 U" in a tribute to Sinead O'Connor, and Fantasia Barrino honoured Tina Turner with her version of "Proud Mary," backed by singers in shiny gold and silver fringed outfits.
Jon Batiste played "Ain't No Sunshine" and "Lean On Me" in a tribute to Clarence Avant, known as "the Godfather of Black music."
Near the start of the show, country star Luke Combs sang his cover hit "Fast Car," alongside the original singer and writer of the 1988 song, Tracy Chapman.
Toward the end, Billy Joel performed his new single "Turn The Lights Back On," his first original song in 17 years.
In accepting the Dr. Dre Global Impact Award, rapper Jay-Z aired some Grammy grievances, including the fact that his superstar wife Beyonce had never won album of the year despite having earned more Grammys than anyone else.
"I don’t want to embarrass this young lady," Jay-Z said as Beyonce watched from the audience. "But she has more Grammys than anyone and never won album of the year. So even by your own metrics, that doesn’t work."
