SirElton John was also presented with an icon award - with a medley of hits performed in his honour.
The masked, in-person event at the Dolby Theatre in Los Angeles, was hosted by R&B star Usher.
The biggest award of the night, song of the year, was won by The Weeknd for his hit Blinding Lights.
Accepting the prize, the Canadian superstar hinted at new music following the success of his most recent album After Hours.
He said: “The After Hours are done and the dawn is coming.”
At the event, the Weeknd performed with newly-married Ariana Grande.
Pop star Grande, 27, tied the knot with Los Angeles real estate agent Dalton Gomez on May 15 during an intimate ceremony with fewer than 20 guests.
She showed off her wedding ring during her performance with The Weeknd for their duet Save Your Tears.
The Weeknd also won male artist of the year, while British star Lipa took home the female equivalent and Swift won best pop album for lockdown record Folklore.
Accepting the prize in a video message, Swift said: “I have to say thank you to the fans for making this album what it was because we all needed to escape into stories, whether it was movies or TV or film or music and the fact that you chose this album, I am so honoured by that.
“And you really wrapped your arms around it, the way that someday we’ll get to wrap our arms around each other when we see each other again, so I’m sending you the biggest hug.”
There were also live performances from Usher, Bruno Mars, Anderson .Paak and Doja Cat.
The latter was named best new pop artist while Roddy Ricch won hip hop artist of the year.
Megan Thee Stallion was the first winner during the televised ceremony as she picked up the award for best collaboration for Savage, her chart-topping track with Beyonce.
Sir Elton John was honoured with the iHeartRadio icon award and was introduced to the stage by Coldplay frontman Chris Martin and hip-hop star Lil Nas X.
John used his speech to talk about young artists as he praised Lil Nas X.
"I'm very humbled because when I first came to Los Angeles in 1970, radio was so important. I'd never heard of radio in America before because I've never been here before, but it was just incredible to me. In England, we had one station," the 74-year-old said.
"Being played on the radio, for the first time, you hear yourself and you're so excited. What this award means is that I still cover new artists," he added. "That's what my life's about now. And when I do my shows, I try and promote young artists because they need exposure, they need the radio. I've had my time, as they say. I'm still glad people play my records, and I love that."
Brandi Carlile, Demi Lovato and H.E.R. performed a musical tribute to the veteran English rocker, with a medley of his hits Bennie And The Jets, Don’t Let The Sun Go Down On Me and I’m Still Standing.
Now in its eighth year, the iHeartRadio Music Awards celebrated the most-played artists and songs on iHeartRadio stations and the iHeartRadio app throughout 2020.