Tyree played trombone and vibraphone with local Texas bands before moving in the early 1930s to Washington, D.C., where he performed with several prominent bands of theswing era.[1] He played withBob Young (1930), and then he joinedTommy Myles's band (1934–36).After he left Myles, he moved to theWest Coast, playing with groups headed byCharlie Echols (1936). Further, he played withEddie Barefield (1936),Eddie Mallory's band (1937) andBenny Carter (1937) and played withCab Calloway from 1939 to 1946.[1]
He toured Europe withDon Redman's big band (1946). From 1947 to 1951, he played withDuke Ellington as a wah-wah trombonist in the style originating withTricky Sam Nanton and Ellington's only vibraphonist, being well-featured on theLiberian Suite.[1] After, he played also withHoward Biggs's Orchestra.
During the 1950s, Glenn did studio work,[1] led his quartet at the Embers, did some television, radio and acting work, and freelanced in swing and Dixieland settings. In 1953, he joined Jack Sterling's New York daily radio show, with which he remained until 1963. During 1965–68, he toured the world withLouis Armstrong's All-Stars and played until Armstrong died in 1971.[1] Later, Glenn led his own group during his last few years.[1]
He was also a studio musician and actor. He wrote "Sultry Serenade", which was recorded byDuke Ellington andErroll Garner.[1] With a lyric added byAllan Roberts, this song became known as "How Could You Do a Thing Like That to Me?" and was recorded byFrank Sinatra.[1]
Glenn lived inEnglewood, New Jersey,[4] where he died of cancer at the age of 61. He was survived by two sons, Tyree Jr., and Roger, both musicians.[1]