Wright was born in Texarkana, Texas,[citation needed] and grew up in Kansas City, where he played with Bennie Moten's band in 1923.
He relocated to New York City in 1927 to play with The Missourians, staying with the group after Cab Calloway became its leader.
Wright remained Calloway's lead trumpeter until 1942 and continued playing with him sporadically through the rest of the 1940s.
Wright also played with Don Redman (1943), Claude Hopkins (1944–1946), Cootie Williams (1944), Lucky Millinder (1946–1952), Sy Oliver (1947), and Louis Armstrong.
In the 1950s and 1960s he taught music and worked as a studio musician, in addition to recording with Arnett Cobb (1951), Count Basie (1951), the Sauter-Finegan Orchestra (1957), and George Shearing (1959).