Kelly cleared waivers Thursday and was sent outright to Triple-A Albuquerque.
The Rockies claimed Kelly off waivers from the Rangers on Monday.
The Rangers designated Kelly for assignment Monday.
Kelly (shoulder) was reinstated from the 7-day injured list Friday and struck out one over a scoreless inning of relief in Triple-A Round Rock's 13-1 win over Albuquerque.
Kelly (undisclosed) threw a bullpen session Tuesday and is nearing a return, Jeff Wilson of RangersToday.com reports.
The Rangers optioned Kelly to Triple-A Round Rock on Sunday, Jeff Wilson of RangersToday.com reports.
The Rangers selected Kelly to their 40-man roster Tuesday.