Johnson played college football at the University of Tennessee, where he was the first recruit of Tennessee coach Doug Dickey. He was named both All-Southeastern Conference (SEC) and All-American in 1966 and again in 1967. He earned the Jacobs Trophy, given to the SEC's best blocker, and he was named the SEC's Most Outstanding Lineman by the Birmingham Touchdown Club. Johnson finished sixth in the Heisman Trophy voting as a center.
Also in 1967, he was named an Academic All-American and was vice president of his class while earning a degree in industrial engineering.
He was the first player chosen by the Bengals in their initial season. He was the second pick overall in the draft, preceded by future Hall of Famer Ron Yary. He was the second highest-drafted center ever selected in an NFL Draft, after Ki Aldrich in 1939.
Johnson was the last original Bengal to retire, after the 1978 season. His uniform number 54 was retired by the team, and remains the only number the team has retired. However, he came out of retirement in 1979 when Bengals center Blair Bush suffered a knee injury and the Bengals asked Johnson to return as a long snapper on punts, field goals and extra points.
Following his retirement as a player, Johnson worked as a color analyst on Bengals radio from 1981 to 1985.