Galloway, the son of Lee Roy and Ruby Galloway of Tuscaloosa, graduated from Holt High School in 1955 and earned his bachelor of science at the University of Alabama in 1959. He performed as a member of the Million Dollar Band and the Cavaliers jazz band.
Galloway began his career at McAdory High School in 1959. In 1962 he was hired as the first band director for Hoover's Berry High School, and completed his master of arts at Alabama in 1963. During that decade he led the Ted Galloway Dance Band with a regular engagement at the downtown Birmingham Elks' Lodge.
In 1970 Galloway was invited to create the band program at the new Vestavia Hills High School. He went on to author an instructional book on jazz improvisation and completed a doctorate in education from the University in 1985.
Galloway's bands consistently excelled in competitions and state, regional and national festivals. His jazz bands were especially well-regarded. He frequently served as judge, clinician or conductor for Southeast US and European jazz programs. He organized the Alabama Lions All-Star High School Marching Band for the 1980 Lions International Convention. He served as president of the Alabama Bandmasters Association and was inducted into the Alabama Jazz Hall of Fame in 1988 and the Phi Beta Mu Alabama Bandmasters Hall of Fame in 1991.
- Galloway, Ted (1984) Basic Jazz Improvisation: B-Flat Book. Alfred Publishing Company. ISBN 0757929397
- "Ted Allen Galloway" obituary (December 21, 2009) The Tuscaloosa News