"I am the hopeful black woman who was denied the right to vote. I am the caring white supporter," Common added. "I am the unarmed black kid, who maybe needed a hand, but instead of was given a bullet.
"Selma has awakened my humanity, he continued, thanking Ava DuVernay, Oprah and more.
"I'm so honored to be a part of this amazing film," Legend said. "We're so grateful to write this song."
In the best original score category, Sienna Miller and Vince Vaughn presented the award to Johann Johannsson for The Theory of Everything.