Hampton was signed as a Minor League free agent by the D-backs on Aug. 21 and made four appearances for Reno, allowing one run on three hits in 3 1/3 innings.
The 37-year-old is 148-115 with a 4.07 ERA in 409 games (355 starts) over a 15-year Major League career with the Mariners, Astros, Mets, Rockies and Braves.
Injuries have hit Hampton hard in recent years as he missed the entire 2006 and '07 seasons after undergoing Tommy John surgery, and he underwent shoulder surgery last September.
Kroenke was selected by the D-backs in last December's Rule 5 Draft. He did not make the team out of Spring Training, cleared waivers and was assigned to Reno. Kroenke spent the season there posting a 7-3 record and a 3.51 ERA. He started nine games and appeared in relief in 31.
The D-backs had promoted three players Wednesday from Reno -- pitcher Carlos Rosa, infielder/outfielder Brandon Allen and infielder Tony Abreu. Another hurler, Leo Rosales, was activated from the 60-day disabled list.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.