Tepesch, 27, was assigned to Triple-A Omaha. To make room on the 40-man roster, the Royals moved right-hander Kris Medlen to the 60-day disabled list -- that move won't affect Medlen's return because he already has spent over 60 straight days on the DL.
Tepesch, originally drafted by the Rangers, is joining his fourth organization this year. He has previously been with the Rangers, Dodgers and A's. He got a Major League start with the Dodgers on June 24 and lost to the Pirates, giving up five earned runs in four innings.
In his Minor League stints this season, Tepesch went 8-3 with a 3.96 ERA over 17 starts.
"It's just starting depth for us right now," Royals general manager Dayton Moore said.
Tepesch is primarily a sinker-slider type pitcher whose fastball velocity ranges 88-92 mph generally.
Jeffrey Flanagan has covered the Royals since 1991, and for MLB.com since 2015. Follow him on Twitter @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.