Onana, who was last month told he would be the first-choice shot-stopper for United this season, was made surplus to requirements earlier in September.
His only appearance came in the Carabao Cup third-round exit to Grimsby Town, in which he was at fault for both goals in a humiliating exit on penalties.
Trabzonspor moved to sign the player on loan and personal terms were quickly agreed. The deal runs until the end of the season and does not include an option to buy.
Reports state that the Cameroon international will earn a higher salary at Trabzonspor, who will also pay bonuses and a signing-on fee.
Onana leaves Old Trafford, albeit temporarily for now, after two error-strewn seasons but was treated to exuberant scenes with fans in the city of Trabzon.
Amorim has opted to start Turkish goalkeeper Altay Bayindir ahead of Onana in the Premier League so far this term despite a series of shaky performances, with veteran Tom Heaton also still at the club.
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