Van Horne was born in Mt. Lebanon, Pennsylvania. He attended Fullerton High School in Fullerton, California. His Fullerton football varsity teammates included future NFL New Orleans Saints tight end Hoby Brenner.
He attended the University of Southern California, where he played for the USC Trojans football team from 1977 to 1980. As a senior in 1980, was recognized as a consensus first-team All-American.
The Chicago Bears selected Van Horne in the first round (11th pick overall) of the 1981 NFL Draft, and he played for the Bears from 1981 though 1993. He was a member of the 1985 Chicago Bears team, winners of Super Bowl XX. In his 13 NFL seasons, he played in 186 games for the Bears, and started 169 of them.
Van Horne was married to Eleanor Mondale from 1988 to 1989. He currently lives in the Chicago suburbs.