To make room on their roster, the Cavs waived guard Donald Sloan, who appeared in 20 games for Cleveland this season.
Livingston made four starts for the Wizards this season. He was waived on Sunday by Washington and the Cavs had until 5 p.m. Tuesday to claim him. He averaged 3.7 points, 2.2 rebounds and 2.2 assists in 17 games. The 6-footer has appeared in 341 career NBA games.
Sloan has appeared in 53 games - 11 starts - for Cleveland, which signed him from the Development League in March.
The Cavs play at Washington on Wednesday night. They'll be without center Anderson Varejao, the league's top rebounder, who will miss his fourth straight game with a bruised right knee.