Born in 1931 in Durham, NC, Morgan eventually made his way to Maryland and attended Montgomery Blair High School in Silver Spring before moving on to University of Maryland. From 1956 to 2002, he coached at DeMatha Catholic High School in Hyattsville, MD. At DeMatha he achieved the second most wins as a head coach in the history of basketball on any level. Many of his players went on to play in the NBA, including fellow Washington Metropolitan Basketball Hall of Fame members Adrian Dantley and Danny Ferry. Wootten gained legendary status in 1965, when his DeMatha team beat Lew Alcindor's Power Memorial Academy and ended their 71-game winning streak. His career coaching record was 1,274-192. As the head coach of DeMatha basketball, Wootten won 5 High School National Championships, 22 Washington, D.C. Championships, and 33 Washington Catholic Athletic Conference (WCAC) championships.
Former UCLA basketball coach John Wooden described his admiration for Morgan when he said, "I know of no finer coach at any level – high school, college or pro. I stand in awe of him." Wootten was inducted into the Basketball Hall of Fame in 2000.
During his coaching career at DeMatha, located just two miles away from his alma mater, he received job offers from North Carolina State, Georgetown and American and interest from Duke, Wake Forest, and Virginia. Wootten turned down the offers, according to Sports Illustrated, because the Maryland job, which was not forthcoming, was the only college job he wanted.