Miller's deal is reportedly worth $1 million, according to Jon Heyman of MLB Network.
Miller is in the starting lineup, batting eighth, against the Chicago White Sox on Sunday, per Bell.
In order to make room on the 40-man roster, Danny Salazar has been placed on the 60-day injured list. The right-hander underwent shoulder surgery back in July.
Miller, 29, is expected to be the Opening Day second baseman for Cleveland, with Jason Kipnis shelved with a mild right calf strain.
While traditionally a second baseman, Miller has moved around the diamond, playing first base and shortstop between the Tampa Bay Rays and Milwaukee Brewers last year.
Miller signed a minor-league deal with the Los Angeles Dodgers earlier this spring. Prior to being released late last week, the utility man was being tried out as an outfielder. Back in 2015, Miller made 20 starts with the Seattle Mariners as a center fielder.
Over a six-year career, Miller owns a .239/.313/.409 slash line with 75 home runs and 33 stolen bases in 680 career games.