Brohm, who played quarterback for the Cardinals and grew up in Louisville, said in a statement Wednesday that although "going home was very appealing and meaningful to me, the timing was not ideal."
Brohm received a sweetened deal from Purdue, with a source telling ESPN's Chris Low that he now will make well over $5 million annually (including incentives and bonuses). By comparison, the new deal Brohm received in April took his base salary to $3.8 million this year.
Brohm met with Louisville athletic director Vince Tyra on Tuesday and had been considered a front-runner for the Cardinals' coaching job since Bobby Petrino's firing earlier this month.
"After intense and thorough discussion, I believe it is important to finish the building process we have begun and honor the commitment I made to our football program, players, and recruits," Brohm said. "... I believe that remaining at Purdue is the right thing to do, and I am excited for the challenges ahead."
The Boilermakers are 13-12 in two seasons under Brohm.
Tyra said in a statement that Louisville will continue its search and hopes to make a hire soon.
"While Jeff and I had a terrific conversation about the future of the University of Louisville football program and how he could play a role in our success, it was clear that his heart and mind were still with fulfilling his commitment to Purdue," Tyra said in a statement. "As a Cardinal alumnus, Jeff has accomplished a great deal as a player and as a coach. We wish him the best going forward except when we may meet on the field of play."
Appalachian State's Scott Satterfield will be one of the coaches Louisville now targets, a source told Low.
Brohm's announcement came shortly after Big Ten officials announced fifth-year senior David Blough was named the third-team all-conference quarterback by the media and Purdue's star receiver Rondale Moore was named the conference's freshman of the year.
Moore grew up in New Albany, Indiana, just across the river from Kentucky, and played at Louisville Trinity, the high school Brohm attended. He now becomes the foundation for Brohm's next chapter at Purdue.
The Associated Press contributed to this report.