A standout linebacker at Duke, he was drafted in 1967 by the Cleveland Browns in the first round of the NFL Draft, which was the final year in which the NFL and the AFL held separate drafts. He was then acquired by the Dolphins prior to the 1971 season, after Miami defensive coordinator Bill Arnsparger requested head coach Don Shula to do so.
He was a member of the 1972 undefeated team for the Dolphins.
Matheson was often used by the Dolphins as a fourth linebacker in passing situations. This defensive alignment was often referred to as the "53" defense, named for Matheson's #53 jersey number. This is also referred to as a "34 defense" based on there being 3 linemen and 4 linebackers.
After leaving the Dolphins in 1979, Matheson returned to Duke as an assistant coach. He also coached two seasons with the Miami Dolphins.