The Cubs announced last week that Adduci has been hired as the organization's run production coordinator, signaling the end of his playing career, Mark Gonzales of the Chicago Tribune reports.
Adduci agreed to a minor-league deal with the Rangers on Thursday, Andersen Pickard of MLBDailyDish.com reports.
Adduci cleared waivers and was outrighted to Triple-A Iowa on Wednesday.
Adduci was optioned to Triple-A Iowa on Monday, Jesse Rogers of ESPN.com reports.
Adduci is starting in right field and batting fifth in Monday's game against the Astros.
Adduci was recalled by the Cubs Monday, Mark Gonzales of the Chicago Tribune reports.
The Cubs reassigned Adduci to their minor-league camp Saturday, Jordan Bastian of MLB.com reports.
Adduci agreed Wednesday with the Cubs on a minor-league contract, Brandon Warne of ZoneCoverage.com reports.
Adduci elected free agency Thursday.
Adduci is out of the lineup for Sunday's series finale against the Royals, Evan Woodbery of MLive.com reports.