Greenidge was born in Cedros, Trinidad and Tobago, in 1937. He studied Architectural Draughtsmanship and Building Design at BIET AND UBOT Training School in Palo Seco but was mostly a self taught artist. He’d instinctively been drawn to drawing and painting as a child, but developed more seriously from 1960 onwards. In 1957 he joined the Southern Art Society (SAS) and later the Trinidad Art Society.  Irish artist, Brother Fergus Griffin of Presentation College as well as the art teacher and founder of SAS and Isaiah Boodhoo, served as major influences in Greenidge’s career. 
Greenidge worked in watercolours and oils. He has exhibited in Trinidad, Brazil, England and Suriname.