Elway, who led the franchise to a pair of Super Bowl titles during his playing career, posted a statement on Twitter after conversations with members of the Broncos organization:
He noted his discussions over the past week changed his perspective.
"I always thought that since I grew up in a locker room, I knew everything there was to know about understanding teammates from different backgrounds and walks of life," he wrote. "What I've realized is that I could not have been more wrong."
Athletes from across the sports spectrum, including those from around the world, have joined the fight.
Broncos linebacker Von Miller was among those to release a statement supporting the movement:
Meanwhile, Denver head coach Vic Fangio received criticism for saying he didn't see racism in the NFL:
He later apologized.
Elway, 59, was the Broncos' quarterback from 1983 through 1998 and returned to the organization in 2011 to serve as general manager.