Frieri will join the Angels before their game on Friday, and the team will announce a corresponding roster move at that time.
Angels general manager Jerry Dipoto has been looking to add bullpen depth since he got the job in November, but his search was intensified when the Angels' bullpen blew six of its first seven save opportunities in April.
"He misses bats," Dipoto said. "He's got a history of missing bats, he's very good at it. He's been in a middle role for the Padres, who've had deep bullpens. It's the opportunity to go find a cost-effective, effective-on-the-field part of a solution."
Frieri, 26, is 1-0 with a 2.31 ERA and leads the Padres bullpen with 18 strikeouts in 11 appearances. A Colombian right-hander, Frieri broke into the big leagues in 2009 and is 3-3 with a 2.33 ERA in 105 major league games.
Amarista, 23, is a speedy, switch-hitting utility guy who had two stints with the Angels, batting .154 in 23 games. Roach, 22, has compiled a 14-6 record and 3.97 ERA in the minor leagues, recently for Class-A Inland Empire.