The Rangers will be without Kela through at least the All-Star break. His DL stint is retroactive to June 30. The 24-year-old was 4-1 with a 2.64 ERA in 30 relief appearances this year. He was riding a nine-inning consecutive scoreless streak, dating back to June 10.
Perez is scheduled to start Monday's opener against the Red Sox in Arlington. The left-hander landed on the DL on June 24 with a fracture and laceration on his right thumb, an injury sustained when he caught his thumb in the hinge of a hotel room door. Perez is 4-6 with a 4.70 ERA in 15 starts in 2017.
The Rangers acquired Grilli in a trade with the Blue Jays on Sunday. The veteran reliever, who pitched in 30 games for Texas in 2009, was 2-4 with one save and a 6.97 ERA in 26 relief appearances for Toronto this year. He was designated for assignment by the Jays on June 27.
Alvarez, 28, owns a 2.76 ERA through 20 appearances across three stints in the big leagues this season.