Gustave was reassigned to minor-league camp Sunday.
Gustave signed a minor-league contract with the Diamondbacks on Tuesday, Robert Murray of FanSided.com reports.
Gustave was placed on the 15-day injured list retroactive to Aug. 1 with right forearm discomfort.
Gustave tossed a clean sixth inning in Tuesday's victory over the Twins.
Gustave (1-0) earned the win Sunday against the Blue Jays, allowing no runs on two hits while striking out none and walking none across two innings.
Gustave (hamstring) was reinstated from the 15-day injured list Saturday.
Gustave (hamstring) will begin a rehab assignment at Triple-A Nashville on Friday.
Gustave is expected to miss around six weeks while recovering from a right hamstring strain, Todd Rosiak of the Milwaukee Journal Sentinel reports.
Gustave suffered a right hamstring injury Saturday and will go on the 15-day injured list, Curt Hogg of the Milwaukee Journal Sentinel reports.