Tannen accepted an athletic scholarship to attend the University of Florida in Gainesville, Florida, where he played defensive back for coach Ray Graves' Florida Gators football team from 1967 to 1969. He developed a reputation for tough play and being brash and cocky. Tannen was a first-team All-Southeastern Conference (SEC) selection in 1968, a first-team All-American in 1969, and the recipient of the Gators' Fergie Ferguson Award recognizing the "senior football player who displays outstanding leadership, character and courage." Memorably, Tannen blocked a punt in the 1969 Gator Bowl, which was returned for a touchdown and provided the Gators' margin of victory in their 14–13 upset win over the Tennessee Volunteers, and helped the Gators achieve their then best-ever record of 9–1–1. A versatile athlete, Tannen finished his three-season college career with eleven interceptions, and led the team in punt return yardage as a senior.
Tannen graduated from Florida with a bachelor's degree in business administration in 1972, and was later inducted into the University of Florida Athletic Hall of Fame as a "Gator Great." In 2006, the sportswriters of The Gainesville Sun chose him as No. 15 among the 100 greatest players from the first 100 years of Florida Gators football.
The New York Jets selected Tannen in the first round (twentieth pick overall) of the 1970 NFL Draft, and he played for the Jets for five seasons from 1970 to 1974. As a rookie, he blocked a punt, recovered the ball and scored against Buffalo in 1970. A series of muscle pulls idled him in 1971. Shoulder injuries slowed him, but he managed to play in thirteen of the games and led the team in interceptions with seven during the 1972 season. In 1973 he managed to start three games at free safety and spent the bulk of the season as backup man at either safety or at cornerback since he had experience at all positions. During his five-year NFL career, Tannen played in sixty-one games and had twelve interceptions with 204 return yards. He was also a standout special teamer, and blocked two field goals and a punt.