Greenwood was born in Canton, Mississippi. He graduated from Arkansas AM&N (now University of Arkansas at Pine Bluff), where he became a member of the Beta Theta Chapter of Phi Beta Sigma fraternity. He was also named the 1968 Ebony All-American defensive lineman in the Southwestern Athletic Conference (SWAC).  Greenwood was drafted by the Pittsburgh Steelers in 1969 in the 10th round. In 1971, he became the starting left defensive end. One of the four members of Pittsburgh’s famous Steel Curtain, he would remain there until retirement in 1981. Greenwood, who was 6 feet 6 inches tall and weighed 245 pounds, was a six-time Pro Bowl player and was named to NFL All-Pro teams in 1974 and 1975. He was named All-AFC five times. He also led the Steelers six times in sacks with a career total of 73½ (sacks were an unofficial stat at the time). According to records kept by the Steelers, Greenwood’s highest single-season sack total was 11, which he attained in 1974. He further had 14 fumble recoveries in his career, including five in 1971, which tied for the NFL lead. He had 4.7 in the 40-yard dash, and that speed allowed him to dominate his position.

In Super Bowl IX against the Minnesota Vikings, Greenwood batted down two passes from Fran Tarkenton. In Super Bowl X against the Dallas Cowboys, he sacked Roger Staubach four times. Greenwood played in all four of the Steelers Super Bowl victories in the 1970s. Unofficially, Greenwood had five sacks in the four Super Bowl appearances.  Greenwood was known for wearing gold-colored shoes on the football field. (By today’s NFL rules, Greenwood would be fined since it would not be in uniform with the rest of the team.) Greenwood was called “Hollywood Bags” because he claimed he kept his bags packed and ready so he could leave for Hollywood at a moment’s notice. He was a finalist in the 2005 Pro Football Hall of Fame voting but did not get elected. He was again a finalist in 2006, but was not elected. Greenwood has stated that while he would be honored if he were to be inducted into the Hall of Fame, he would not be upset if he were not elected, feeling that the Steelers already in the Hall (in particular, “Mean Joe” Greene) represent the entire team’s accomplishments.  In 1991, Greenwood was named to the Super Bowl Silver Anniversary Team and in 2007 he was named to the Steelers All-Time team.