The Diamondbacks released Graterol from his minor-league contract Aug. 1.
The Diamondbacks reassigned Graterol to minor-league camp Sunday.
Graterol was acquired by the Blue Jays from the Angels on Wednesday in exchange for cash considerations.
Graterol and the Angels agreed to a minor-league deal Tuesday, Fabian Ardaya of The Athletic reports.
Graterol signed a minor-league contract with the Twins on Tuesday, Andersen Pickard of MLBDailyDish.com reports.
Graterol declared free agency Monday.
Graterol cleared waivers and was outrighted to Triple-A Louisville on Friday.
Graterol was designated for assignment by the Reds on Wednesday.
Graterol was activated from the concussion injured list Saturday.
Graterol (concussion) was placed on the 7-day injured list Friday.