Koch cleared waivers and was outrighted to Triple-A Albuquerque by the Rockies on Monday, Patrick Lyons of JustBaseball.com reports.
Koch was designated for assignment Friday.
Koch picked up the save in an extra-innings win over Oakland on Wednesday, allowing one walk over one-third of an inning.
The Rockies selected Koch's contract from Triple-A Albuquerque on Sunday, Luke Zahlmann of The Denver Gazette reports.
The Rockies reassigned Koch to minor-league camp Monday.
Koch signed a minor-league contract with the Rockies on Wednesday, Thomas Harding of MLB.com reports.
Koch will be the first pitcher on the mound in what's expected to be a bullpen game for the Rockies against the Twins on Saturday, Luke Zahlmann of The Denver Gazette reports.
Colorado selected Koch's contract from Triple-A Albuquerque on Tuesday.
Koch signed a minor-league contract with the Rockies on Nov. 22 and received an invitation to major-league spring training.
The Mariners outrighted Koch to Triple-A Tacoma after he cleared waivers Thursday.