Minasian's deal, which makes him the 13th general manager in Angels history, is for four years, according to the team. He will be officially introduced in a press conference Tuesday.
"After an expansive process, we are thrilled to announce Perry as our general manager," Angels owner Arte Moreno said in a statement. "His background in scouting and player development along with his unique understanding of roster construction were the leading factors in our decision.
"We are proud to welcome Perry, his wife, Michelle, and their four children to the Angels family."
The 40-year-old Minasian was one of two finalists for the Angels' GM job. He beat out Seattle Mariners assistant general manager Justin Hollander, who previously worked for the Angels for nine years.
Minasian replaces former general manager Billy Eppler, who was fired by the Angels in late September after the club's fifth consecutive losing season. Since 2009, the Angels have qualified for the playoffs only once.
Minasian will be tasked with guiding the Angels to the postseason for the first time since 2014.
"I am humbled and honored to lead the baseball operations of the Los Angeles Angels," Minasian said in a statement. "I am grateful to Arte Moreno, [Angels] president John Carpino, and the entire Angels family for this opportunity. My family and I couldn't be more excited to be a part of this community."
Braves executive Alex Anthopoulos hired Minasian before the 2018 season. Since that year, he has served as Anthopoulos' right-hand man. Atlanta won the NL East in each of Minasian's three seasons with the organization.