The team also purchased the contract of Express pitcher Michael Kirkman. A corresponding roster move has not been made yet, but either Tanner Scheppers or Shin-Soo Choo will be transferred to the 60-day disabled list to make room on the newly expanded 40-man roster for Kirkman.
The moves become official on Tuesday.
Spencer Patton wraps up the initial list of September callups, but he won't join the team until Thursday. The Rangers acquired Patton from the Royals for reliever Jason Frasor in July.
Rangers manager Ron Washington revealed that Tepesch (4.44 ERA, 17 starts) would start Wednesday's finale against Kansas City.
He also offered a ringing endorsement of Kirkman, who Washington plans to use as a situational left-hander after he dominated left-handed hitters at Triple-A.
"He might have to go left-right-left, but I don't think we're going to keep him out there against right-handers," Rangers manager Ron Washington said.
Jackson Alexander is an associate reporter for MLB.com.