Tibesar replaces Gary Emanuel, who was let go after the Boilermakers finished ninth in the Big Ten in total defense and allowed 26.8 points per game.
Tibesar spent the previous three seasons with the Montreal Alouettes of the CFL, where he was promoted to defensive coordinator for the 2011 season.
The Alouettes went 10-8 this season and won the Grey Cup the previous two seasons with Tibesar serving as linebackers coach.
Purdue coach Danny Hope said in a release that Tibesar is "on the cutting edge of the science of defensive football," and that his experience in defending a larger field and 12-man offenses would help the Boilermakers defend against spread offenses
Before heading to Canada, Tibesar worked three seasons at Kansas State, serving as the Wildcats' defensive coordinator in 2007 and 2008.