Middleton confirmed his decision Thursday night.
Middleton left a game against Minnesota last Sunday in the middle of an at-bat after 12 pitches. He had appeared in three games in four days after a stint on the disabled list with elbow inflammation.
Middleton was the Angels' closer in April, recording six saves. He compiled a 2.04 ERA while allowing only four runs in 16 appearances.
Instead, Middleton will become the fifth pitcher on the Angels' current staff to undergo elbow ligament replacement surgery. He joins Andrew Heaney, Tyler Skaggs, Nick Tropeano and JC Ramirez, who was injured in April.