Bjornsson, who portrayed Ser Gregor "The Mountain" Clegane in the HBO series, broke the record at his gym in his native Iceland.
The strongman lifted the barbell for two seconds, before dropping the weights and roaring in delight.
The event was streamed by sports broadcaster ESPN and filmed for Bjornsson's YouTube channel.
Bjornsson, who is 2.05m tall (6ft 9in), previously won the World's Strongest Man competition in 2018.
Speaking in a "behind-the-scenes" video posted on YouTube, Bjornsson said: "I'm extremely proud, you know. I'm extremely happy.
"It's great - there's nothing better than proving people wrong. So many people didn't believe in me, so many people that said, '501kg is never going to go up'... But I also had a lot of support."
He added: "I feel healthy, I feel good. I'm just absolutely speechless, even though I'm talking a lot now. But I'm excited, super excited - this is huge for me."
The record was previously held by Eddie Hall, a British man who in 2016 became the first man to lift 500 kg.