Coming out of high school, Tony Woods was a Consensus All-American. While at Seton Hall Prep School, he was first-team All-State, first-team Parade All-American and first-team All-USA Today All-American his senior year. He played in two consecutive state football championship games.

Woods played collegiate football at the University of Pittsburgh. As a senior, he had 109 tackles, including 18 tackles against Rutgers University. He finished his career as a second-team All-American with 242 tackles and 31 sacks.

Before going to the NFL, Woods spent time in the United States Football League. He was selected 92nd by the Houston Gamblers in the 1986 USFL Draft. Woods was drafted 18th overall in the 1987 NFL Draft by the Seattle Seahawks and the first ever New Jersey football player to be taken in the first round of the NFL draft. He played in Seattle from 1987 to 1992. In 1993, Woods signed with the Los Angeles Rams, where he played for one season. Woods then signed with the Washington Redskins, where he finished his career.

Woods is currently an assistant football coach at William Paterson University.