Greenidge began his career in English county cricket before he played for Barbados. He played for many seasons with Hampshire in the English County Championship, where he batted as an opener with Barry Richards. He was therefore eligible to play for England until he opted for the West Indies. He later made an appearance for Scotland. During his first-class career, he scored a total of 37,000 runs with 92 centuries.

Born in St. Peter, Barbados, Greenidge played as an opening batsman for the West Indies. He began his Test career in 1974 against India at M. Chinnaswamy Stadium, Bangalore. Greenidge and Desmond Haynes formed a prolific opening partnership. The pair made 6,482 runs while batting together in partnerships, the highest total for a batting partnership in Test cricket history.

During the 5th test of the 1983 series between West Indies and India, Greenridge became the first and, as of 2017 only, person in test history to be retired not out. He had to leave the match in Antigua while on 154 to visit his gravely ill daughter, who died two days later, in Barbados.

Greenidge scored two double centuries against England in the 1984 summer Test series. This series was dubbed the "Blackwash" because West Indies won by a margin of 5–0. Greenidge scored 214 not out in the second innings of the second Test at Lord's in June 1984 and followed up with 223 in the fourth Test at Old Trafford in late July. The 214* was achieved on the fifth and last day of the match as West Indies successfully chased 342 for victory. It remains the highest run chase at Lords.

Greenidge became the first player in One Day International (ODI) history to score a century in his 100th ODI when he scored 102* against Pakistan in 1988. In that game he achieved that milestone as captain, with his century eventually going in vain as West Indies lost that match.

In total, Greenidge played in 108 Test matches, scoring 7,558 runs with 19 centuries, and in 128 ODIs, including the 1975 and 1983 World Cup Finals, scoring 5,134 runs and 11 centuries.

Greenidge decided to pursue a coaching career and became the coach of the Bangladeshi national cricket team in 1997. Under his guidance, Bangladesh won the ICC Trophy in 1997. This victory qualified Bangladesh to play in the 1999 Cricket World Cup—their first appearance in top-level cricket. Soon afterwards Greenidge was named an honorary citizen of the country. In 2000, Bangladesh were promoted to ICC full member status and began playing Test cricket.

Greenidge is currently on the West Indies selection committee for Test matches, along with Viv Richards.

Greenidge's son Carl is a form