Redd was born and grew up in New York City; after losing his father at the age of one, he was raised by his mother, who moved around Harlem, Brooklyn and other neighborhoods. An autodidact, he began playing the piano at a young age and took to studying jazz seriously upon hearing Charlie Parker during his military service in Korea in the mid-1940s.
Upon discharge from the Army in 1949, he worked with drummer Johnny Mills, and then in New York played with Tiny Grimes, Cootie Williams, Oscar Pettiford and the Jive Bombers. In 1954, he was playing with Art Blakey. Redd toured Sweden in 1956 with Ernestine Anderson and Rolf Ericson.