Fisch, 44, replaces recently fired head coach Kevin Sumlin.
"We are tremendously excited to have Jedd Fisch come to Tucson to reinvigorate our football program and lead us to championships," Arizona athletic director Dave Heeke said in a statement announcing the hiring. "Jedd has a unique ability to teach the game of football effectively to his players and to inspire them with his passion. We conducted a comprehensive national search with an impressive array of candidates but in the end, Jedd is exactly what our program needs right now and I cannot wait to partner with him to move us forward."
Fisch and San Jose State coach Brent Brennan were the two finalists for the opening.
Fisch, who also was among the finalists when Arizona hired Sumlin in 2018, has a close relationship with university president Robert Robbins.
"I am honored and humbled to lead the University of Arizona football program," Fisch said in the statement. "I am 100% committed to building a program that all Wildcat fans will be proud to support. We will study hard, compete hard, recruit hard and be relentless in all aspects of our program."
Fisch joined the Patriots this year after two seasons with the Los Angeles Rams as a senior offensive assistant. Before joining the Rams, he was UCLA's offensive coordinator for one season. He also has been an offensive coordinator at the NFL level with the Jacksonville Jaguars.
The Wildcats, 0-5 this season, are on a record 12-game losing streak after dropping their final seven games in 2019. The 70 points they allowed to Arizona State marked the most ever surrendered in the Territorial Cup series, dating to 1899.
Arizona went 9-20 -- 6-17 in the Pac-12 -- with no bowl appearances under Sumlin and lost all three games to Arizona State.
ESPN's Adam Rittenberg contributed to this report.