Elmore was announced as the hitting coach for Double-A Clearwater on Tuesday, MLB.com reports.
Elmore was released by the Indians on Friday.
Elmore signed a minor-league contract with Cleveland on Friday and will join the team's 60-man player pool.
The Pirates released Elmore on June 9.
Elmore was outrighted to Triple-A Indianapolis on Friday.
Elmore had his contract selected from Triple-A Indianapolis prior to Tuesday's game against the Mariners, Rob Biertempfel of The Athletic reports.
Elmore cleared waivers and was outrighted to Triple-A Indianapolis on Wednesday.
Elmore was designated for assignment by the Pirates on Sunday, Adam Berry of MLB.com reports.
Emore was recalled from Triple-A Indianapolis on Monday, John Perrotto of DKPittsburghSports.com reports.
Elmore re-signed with the White Sox last week on a minor-league contract, Matt Eddy of Baseball America reports.