Leggett's career as a professional football athlete began as a first-round draft pick of the Chicago Bears in 1957 and spanned 11 years (1957–1968). He is recorded as having played in 132 professional football games.
His career with the Chicago Bears lasted from 1957 to 1965 where he played at both Defensive Tackle and Defensive End positions. He was part of the famed "Monsters of the Midway" defense that led the Bears to the 1963 NFL championship. He was traded to The Los Angeles Rams in 1966 where he played in 10 regular season games with the Los Angeles Rams' "Fearsome Foursome" defense.
Toward the end of his career, journeyman Leggett played 20 games in 1967 & 1968 for the expansion New Orleans Saints franchise. While statistics on sacks were not recorded back then, www.pro-football-reference.com credits Leggett with 16 fumble recoveries, 1 safety and 1 interception.
Leggett was a good friend to many and did outstanding community service in the Mississippi area and Gulf Coast region. He first played college football at Hinds Jr. College (today known as Hinds Community College) which was the only school that would give him a chance due to academic circumstances. He started playing for them at 16 (which was then legal) and was able to raise his academic standing to get into Louisiana State University. Leggett became an All-Southeastern Conference player at LSU. Leggett had an amazing wife, 4 kids 2 boys and 2 girl's, and 14 grand kids.