He attended Bryan Station High School in Lexington, where he was a nationally-ranked track and field performer in the discus and shot put. During his junior year, he joined the football team as a favor to his friends, where he was successful as a guard. Although he had still planned to attend college on a track scholarship, recruiters at the University of Kentucky convinced him to attend on a football scholarship.
Dawson was picked by the Steelers in the second round of the 1988 NFL draft, and played on the offensive line alongside Hall of Famer Mike Webster, from whom he took over the role of starting center the next year.
He soon became one of the most respected players among the Steelers, and one of the best in the league at his position. His friendly demeanor earned him the nickname Ned Flanders, after the character from The Simpsons.
Dawson was named to seven straight Pro Bowls from 1992 to 1998 and played in 171 consecutive games, until severe hamstring injuries forced him to sit out nine games in 1999 and seven more games in 2000. Dawson was released by the Steelers following the 2000 season partly due to these injuries and partly due to salary cap reasons, but opted to retire rather than trying to play for another team.
Dawson lives in Lexington, where he is a real estate developer. He is on the Board of Trustees at his alma mater, the University of Kentucky. He is married, with two children.
Although the Steelers do not officially retire numbers, Pittsburgh has not reissued Dawson's number 63 jersey since his retirement.
Dawson was one of twenty-five finalists for the Pro Football Hall of Fame in 2005, his first year of eligibility, as well as in 2006 and 2007.