"I called them last night and said I'd take the job," English told the Associated Press on Tuesday, the day the Wolverines beat Florida 41-35 in the Capital One Bowl. "I've appreciated my time at the University of Michigan, particularly the opportunity to work with coach Lloyd Carr, a man I love."
English agreed to a two-year contract with the Cardinals, who finished the season at 6-6.
On Nov. 19, Carr said he was retiring after the season, ending his 13-year stint as head coach and 28-year stay on the staff.
Rodriguez, who left West Virginia to succeed Carr, fired all of Michigan's assistants shortly after he was hired last month and has rehired only one coach: Fred Jackson, who will have a role on the offensive staff.
English had denied accepting the position with the Cardinals previously, in part because he was aggressively being pursued by UCLA and Washington.
The Cardinals fired defensive coordinator Mike Cassity following Louisville's disappointing 6-6 season in which the defense finished 84th in the country in total defense and 93rd in scoring defense.
"I'm excited about the opportunity at Louisville, where I'm going to get another chance to prove that I can affect change," English said. "We need to change the personality of the defense and I can't wait to get started."
English was on Carr's staff for five seasons, the last two as defensive coordinator and being named Rivals.com defensive coordinator of the year in 2006. He started at Michigan as its secondary coach after being an assistant at Arizona State, San Diego State and Northern Arizona.
He earned four letters at California, starting at safety for the Bears as a senior and ending his playing career in the 1990 Copper Bowl.