The Bridge of Spies actor beat out Christian Bale in The Big Short, Tom Hardy in The Revenant, Mark Ruffalo in Spotlight and Sylvester Stallone in Creed.
"I've always just adored stories: hearing them, seeing them, being in them," he said, thanking director Steven Spielberg. "Unlike some of the leaders we're being presented with these days, he leads with such love that he's surrounded by masters in every craft."
Rylance also joked that acting alongside Tom Hanks "clearly helps," saluted his fellow nominees and concluded, "It's a wonderful time to be an actor and I'm proud to be part of it."
The awards are being handed out at the Dolby Theatre in Hollywood. Chris Rock is hosting.
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