The superstar had previously been tied on three best album wins with Stevie Wonder, Paul Simon and Frank Sinatra.
She received the prize from Celine Dion, who made an unexpected appearance amid health fears. Swift also used the event to reveal a surprise new album.
Miley Cyrus and Billie Eilish took the other top awards at Sunday’s ceremony.
The Los Angeles show was dominated by women, with R&B stars SZA and Victoria Monét and all-female indie supergroup Boygenius picking up multiple awards, and music icons Tracy Chapman and Joni Mitchell giving rare and poignant performances.
Killer Mike was the top male winner, taking three rap trophies. But his success was overshadowed by an apparent altercation backstage, which led to him being booked on a misdemeanour charge.
Song of the year is different to record of the year – the former recognises songwriters and achievement in composition while the latter is concerned with the technical recording process – taking into account production, engineering and performance.
Dion got a rapturous reception when she emerged to present the best album trophy, almost a year after she was forced to cancel all of her live shows after being diagnosed with a rare neurological disorder.
“When I say that I’m happy to be here, I really mean it from my heart,” she told the audience.
There was an equally enthusiastic response when Dion announced Swift’s name as the winner of best album.
The historic achievement is one of many the star has notched up in recent years. She said she “would love to tell you that this is the best moment in my life”, but that simply finishing a song, rehearsing or preparing to play a show makes her equally happy.
For me, the award is the work,” she said. “All I want to do is keep being able to do this. I love it so much. It makes me so happy. It makes me unbelievably blown away that it makes some people happy who voted for this award too.”
Swift previously won album of the year in 2010 for Fearless, in 2016 for 1989, and in 2021 for Folklore.
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