Catlett played for West Virginia from 1959 to 1963. During his tenure playing there, he helped the Mountaineers to two NCAA tournament berths. After he graduated in 1963, he began his coaching career. He started out with assistant coaching jobs at Richmond, Davidson, Kansas, and Kentucky.
In 1972 he was named head coach of University of Cincinnati. In six seasons there, he took Cincinnati to three NCAA tournament appearances and one NIT appearance. He left Cincinnati under a cloud after the basketball program was penalized by the NCAA for numerous recruiting violations during his tenure. His teams were eliminated in the first round of the 1976 and 1977 NCAA tournaments despite being highly ranked.
In 1978 he took over the head coaching job at WVU. Over the next 24 years, he posted a 439-276 record, and a career 565-320 record. Catlett's West Virginia teams won an average of 19 games a season and made eight trips to the NCAA tournament, including a 1998 Sweet 16 appearance.
In 1997, Catlett was nominated as the Big East Coach of the Year, but failed to win as John MacLeod took that honor.
Catlett retired after a 78-63 loss to Virginia Tech on February 13, 2002. 
In late 2005 he publicly stated that he was considering running in the 2006 Republican primary in order to challenge incumbent Democratic Senator Robert Byrd. He later declined to run.