Minasian spent the past three years with the Atlanta Braves as the organization's assistant general manager.
He replaces Billy Eppler, who was fired in September following five straight losing seasons.
Los Angeles finished 2020 with a 26-34 record, missing even the expanded postseason to mark six straight years without reaching the playoffs.
Mike Trout has been one of the best individual players in baseball during his nine full years in the majors, but he has only one postseason appearance in 2014 and the team was swept in the first round.
Even with aggressive moves to add players like Albert Pujols and Shohei Ohtani, the squad hasn't found much success on the field.
Minasian will try to turn things around after helping build the Braves into one of the top teams in the majors. Atlanta went 72-90 in 2017 but has reached the playoffs in each of the last three years, going to the NLCS in 2020 before losing to the eventual champions Los Angeles Dodgers in seven games.
Before joining Atlanta, Minasian spent nine years with the Toronto Blue Jays, starting as a Major League scout and then becoming the director of scouting. He also grew up around the Texas Rangers with his father serving as a clubhouse manager.
It gives him a lot of experience around baseball heading into his new role.
The Angels also had Seattle Mariners assistant GM Justin Hollander, Chicago Cubs senior vice president Jason McLeod and Arizona Diamondbacks assistant GMs Jared Porter and Amiel Sawdaye for second interviews before deciding on Minasian, per Alden Gonzalez of ESPN.