Dawkins won the award Thursday night at the NFL Players Association gala in Washington, D.C.
Dawkins received the award as the NFL player who best served his team, community and country in the spirit of White, who was a Supreme Court justice, pro football player and humanitarian.
"This is an absolute blessing," said Dawkins, whose wife, Connie, accepted the award on his behalf.
Dawkins, who joined the Broncos this spring as a free agent, served as regional spokesman for the Juvenile Diabetes Research Foundation while in Philadelphia. He also worked with the Burn Prevention Foundation, hosting an annual golf tournament to raise awareness and money for its programs.