Pop singer Eilish claimed the artist prize on Monday over Taylor Swift, Kendrick Lamar, Morgan Wallen and other nominees.
Eilish won all seven categories in which she was nominated, including album of the year and favourite touring artist.
"This is so crazy. I feel speechless," Eilish said in a video message from Europe, where she is on tour.
"I wish I could be there tonight."
Eilish, 23, released her third studio album, Hit Me Hard and Soft, in May 2024.
That's So True singer Gracie Abrams, winner of new artist of the year, also sent a recording to accept her honour. She thanked her fans, who she said "I have been lucky enough to learn from".
"They have reminded me of the light that exists out there," Abrams said.
SZA took home AMA accolades for female R&B artist and for R&B song for Saturn.
Becky G was named favourite female Latin artist.
Many big names on the nominees' list didn't attend the show, which was broadcast live on CBS from the Fontainebleau Las Vegas hotel.
One absentee was Beyonce who claimed favourite female country artist and favourite country album for Cowboy Carter, her first AMA wins in country categories.
Post Malone was named favourite male country artist.
Other no-shows included Taylor Swift and Kendrick Lamar.
Lamar went into the ceremony with a leading 10 nominations. He earned one award, favourite hip-hop song, for Not Like Us.
The festivities opened with host Jennifer Lopez singing and dancing to a six-minute medley of 23 hits by the nominees.
The songs included Eilish's Birds of a Feather, Sabrina Carpenter's Espresso and Beyonce's Texas Hold 'Em.
Janet Jackson was honoured with the Icon award, a tribute for artists with global influence.
"I don't consider myself an icon," Jackson said on stage.
"The one thing that I hope for is that I'm an inspiration for others to follow their dreams and succeed."
Eighty-year-old Rod Stewart received a lifetime achievement honour and danced and sang to his pop hit Forever Young, which was released in 1984.
Stewart said that when he started his career "I had this burning ambition to sing".
"That's all I wanted to do. I didn't want to be rich or famous," he said.
