The 36-year-old left-hander signed with the Indians on Saturday and pitched in two games over the weekend, allowing two hits in 2 1/3 scoreless innings at Minnesota.
Cleveland has used 16 relievers this season and has the highest bullpen ERA at 6.02.
Perez has a $250,000 salary should he pitch in the minor leagues under the deal. In the majors, he can earn $650,000 in performance bonuses based on games: $50,000 each for 10, 15 and 20, and $100,000 apiece for 25, 30, 35, 40 and 45.
He had a 2.57 ERA in 16 games this season for New York Yankees' Triple-A team at Scranton/Wilkes-Barre. Perez had a 4.95 ERA in 64 appearances last year for Washington.
Cleveland is Perez's eighth major league team. Perez debuted in 2002 with San Diego as a starter and has a career 4.46 ERA in 1,369 1/3 innings.