The 39-year-old Redmond had appeared in just three games since June 8. He made his major league debut with Florida in 1998.
Indians manager Manny Acta says the way this season has gone, the team is focusing on developing its younger players. Cleveland, last in the AL Central, has lost several key players, including center fielder Grady Sizemore, to injuries.
The 27-year-old Gimenez also can play first base and the corner outfield positions.
The Indians made the moves before Saturday night's game at Tampa Bay.
Copyright 2010 by The Associated Press
This story is from ESPN.com's automated news wire. Wire index