Earlier, Swift's re-recording of her 2012 record "Red" took the trophy for favorite pop album. The 32-year-old singer has been making new versions of albums from her past after a dispute with her former record label.
"I cannot tell you how much my re-recorded albums mean to me, but I never expected or assumed they'd mean anything to you," she said.
Swift did not mention last week's controversy over Ticketmaster's sales for her upcoming tour, which were filled with glitches and prompted the company to apologize to her.
In the artist of the year category, Swift triumphed over formidable names including Beyonce, Harry Styles, The Weeknd, Drake, Adele and Bad Bunny.
Singer Pink opened the awards show dancing and singing on roller skates to her upbeat song "Never Gonna Not Dance Again."
Comedian and host Wayne Brady rapped in his monologue. "Ain’t nobody getting slapped tonight," Brady joked, referencing Will Smith's infamous attack on Chris Rock at the Oscars.
Dove Cameron, a former Disney Channel actress who reached the Billboard charts this year with the pop single "Boyfriend," earned the first trophy of the night with her best new artist win.
Machine Gun Kelly, wearing a purple suit with long silver spikes, was named favorite rock artist.