The loan deal includes an option for Manchester United to recall Vitek in January.
Vitek had recently signed a new contract with Manchester United, which will keep him with the club until 2028.
On joining Bristol City, Vitek expressed his excitement, saying that the Championship league is a new level for him.
He also looks forward to playing more games and getting to know the team and staff better.
Bristol City's Technical Director, Brian Tinnion, welcomed Vitek, saying that he is a highly regarded goalkeeper from Manchester United.
Tinnion is pleased to have Vitek join the team, as he believes Vitek will strengthen the goalkeeping department for the upcoming season.