Dawson, the 77-year-old seventh son of a seventh son, was voted into the Hall of Fame in 1987 after a 19-year professional playing career. That career was mostly with the Kansas City Chiefs, whom Dawson led to the win in Super Bowl IV.
After retiring as a player, Dawson started a career as a broadcaster with Kansas City, Mo., television station KMBC. He still serves as an analyst on the Chiefs radio network.
He also worked on HBO's "Inside the NFL" (1977-2001).
"This is an unbelievable award for me," Dawson said in a statement Thursday. "To be in the Hall of Fame as a player was the highlight of my playing career but now to be recognized by the Hall of Fame as a broadcaster, well, it's just a great, great honor."
The Pete Rozelle Radio-Television Award is given for "long-time exceptional contributions to radio and television in professional football."
Dawson will receive the Rozelle Award Aug. 3, two days before the Pro Football Hall of Fame induction ceremonies.