The Rockies selected Koch's contract from Triple-A Albuquerque on Sunday, Luke Zahlmann of The Denver Gazette reports.
The right-hander missed Colorado's Opening Day roster but will join the big-league club after making 18 appearances for Albuquerque. Koch has posted a 2.53 ERA, 1.09 WHIP and 15:2 K:BB across 21.1 innings in the minors this season.