Kelly cleared waivers Saturday and was sent outright to Triple-A Louisville.
The Reds designated Kelly for assignment Thursday.
Kelly was credited with a save in Saturday's 10-2 win over the Pirates after striking out two batters over three perfect innings of relief.
The Reds selected Kelly's contract from Triple-A Louisville on Saturday.
The Reds signed Kelly to a minor-league contract Wednesday.
Kelly re-signed Wednesday with the LG Twins of the Korea Baseball Organization, Jee-ho Yoo of the Yonhap News Agency reports.
Kelly signed a contract with the LG Twins of the Korean Baseball Organization on Tuesday, Dan Kurtz of MyKBO.net reports.
Kelly (0-3) took the loss while limiting the Padres to two runs on six hits with three strikeouts over five innings Wednesday.
Kelly will start Wednesday's contest against San Diego, Yahoo! Sports reports.
Kelly could start Sept. 26 against San Diego, Kerry Crowley of The San Jose Mercury News reports.