Elliott was an All-American quarterback on the undefeated 1948 Michigan Wolverines football team that won a national championship.

[1] Elliott is the only Michigan athlete to have earned 12 letters in varsity sports: football, basketball, and golf.

With the Illini, his record was 31–34–1, earning a Big Ten title and Rose Bowl victory over Washington during the 1963 season.

He, along with basketball coaches Harry Combes and Howie Braun, was pressured into resigning on March 19, 1967, by the university which was threatened with expulsion by the Big Ten Conference over a slush fund scandal.

In March 1978, Elliott rejoined his former boss, Bud Wilkinson, as an assistant with the NFL St. Louis Cardinals.