Cooper grew up in the Knoxville suburb of Powell, Tennessee and joined the United States Army after high school. After serving for two years, he enrolled at Iowa State University where he played football for four years eventually becoming team captain and MVP.

Cooper spent time as an assistant coach at Iowa State, Oregon State, UCLA, Kansas, and Kentucky. In 1977, he was named the head football coach at the University of Tulsa, where he compiled a 57-31 record with five Missouri Valley Conference titles. He became the head coach at Arizona State in 1985 where his teams won three consecutive bowl games, including the 1987 Rose Bowl, during his three year tenure. He accepted the job as head coach at Ohio State on December 31, 1987. It is rumored that he became the front-runner for the head coaching position at Ohio State because of his 1987 Rose Bowl victory over Michigan.

During his time in Columbus, he never won an outright Big Ten championship, but shared Big Ten titles in 1993, 1996, and 1998. Unfortunately, Cooper will never be remembered for his many victories at Ohio State, but instead will be remembered for his 2-10-1 record against archrival Michigan. His most crippling losses to the Wolverines came in 1993, 1995, and 1996. In 1993, Ohio State entered the game undefeated, ranked #5, and heavily favored, only to be shutout by the Wolverines and denied their first trip to Pasedena in almost 10 years. In 1995, Ohio State lost a #2 ranking, the Big Ten Title, and another shot at the Rose Bowl by losing to the Wolverines in Ann Arbor. In 1996, the Buckeyes smelled revenge in Columbus and were ranked #1, but failed to achieve payback. The 1996 gut-wrenching loss prevented a #1 vs. #2 matchup in the Rose Bowl against Cooper's former team, Arizona State. His dismal record against Michigan, coupled with a poor bowl record and pervasive academic and discipline problems amongst his players, led to Cooper's firing after the 2000 season. In his 13 seasons, Cooper compiled an impressive 111-43 won-loss record. He is currently a college football analyst for ESPN.

Cooper recruited and coached a great deal of talent that would go on to play in the National Football League, including 1995 Heisman Trophy winner Eddie George, 1996 Outland Trophy winner Orlando Pace, Alonzo Spellman, Robert Smith, Dan Wilkinson, Joey Galloway, Terry Glenn, Mike Vrabel, David Boston, Shawn Springs, Antoine Winfield, Ahmed Plummer, Na’il Diggs, Nate Clements, and Ryan Pickett.