During his 1992 senior year of high school Delk was named "Mr. Basketball" in the state of Tennessee and also to the Parade and McDonald's All-American Teams. As a sophomore at Kentucky, Delk was voted All-SEC 2nd Team by the coaches and All-SEC 3rd Team by the Associated Press, while also making the All-SEC Tournament Team for his outstanding play. Delk was named to the All-SEC 1st and All-NCAA Regional teams during the 1994-95 season. In the 1995-96 season, Delk was named to the All-American and All-SEC 1st Teams and was named NCAA Basketball Tournament Most Outstanding Player. He received SEC Player of the Year honors during the season. Delk joined Omega Psi PhiFraternity while at Kentucky.
Tony Delk is the uncle of current Mississippi State University basketball-playing twins Richard and Reginald Delk. He also sponsors the Tony Delk Legends Game, a benefit for the Taylor Delk Sickle Cell Foundation.