Ossenfort interviewed Friday with a panel of Cardinals executives, including owner Michael Bidwill, after an initial phone conversation with Bidwill days earlier.
Ossenfort, 44, brings 21 years of experience to Arizona. He was with the Titans for the past three years and the New England Patriots for the 15 years before that.
"It was critically-important for us to find the right person to lead us as general manager and there is no doubt in my mind that we have that in Monti Ossenfort," Bidwill said in a statement. "He possesses every attribute of a successful GM -- passion, leadership, intelligence, work ethic -- and his extensive experience has clearly prepared him for this role.
"We could not be more thrilled to have Monti and his family joining the Cardinals."
During his tenure in Tennessee, the Titans made the playoffs in 2020 and 2021, winning the AFC South in both years. While Ossenfort was with the Patriots, where he ascended from personnel assistant to director of college scouting, New England won four Super Bowls and went to three others.
Arizona fired coach Kliff Kingsbury on Jan. 9, the same day the team announced that former general manager Steve Keim had stepped away from the organization "in order to focus on his health."
The Cardinals went 4-13 this season. Kyler Murray had surgery to repair his torn right ACL earlier this month, with Kingsbury saying at the time that the QB "probably" won't be back for the start of the 2023 season.