Texas made the move before its game Friday night against Kansas City.
Tolleson was 2-2 with a 7.68 ERA in 37 relief appearances this season. The right-hander had 35 saves in 2015 and 11 more this season before four blown chances. After Tolleson blew saves in consecutive appearances in mid-May, Sam Dyson took over as the closer.
Harrell, who is expected to start Sunday for the Rangers, and left-handed reliever Dario Alvarez were acquired Wednesday in a trade with Atlanta for a minor league infielder.