Perez, who racked up 124 saves over four-plus seasons with Cleveland, inked a deal worth $2.3 million, ESPN.com reported.
The 28-year-old has a career 15-21 record with a 3.41 ERA and 132 saves over 344 games with Cleveland and the St. Louis Cardinals. He went 5-3 with a 4.33 ERA and 25 saves in 54 games for Cleveland in 2013, but lost the closer's job due to a rough second half and was subsequently released.
Perez and his wife were found guilty of misdemeanor marijuana possession in September. and he antagonized team ownership and fans with critical remarks about poor attendance at Indians games.
The Dodgers Tuesday also announced the signing of veteran reliever Jamey Wright, who finished 2-2 with a 3.09 ERA in 66 games for Tampa Bay last season.
Wright, 39, played for the Dodgers in 2012, compiling a 5-3 record with a 3.72 ERA in 66 appearances.