The 21-year-old has been training with the first team at Carrington and put pen-to-paper on a deal that runs until 2028.
Instead of embarking on Tour 2025, presented by Snapdragon, he has been finalising a temporary switch that should provide valuable experience in the Championship.
The Ashton Gate outfit finished last term in sixth spot in England's second tier, before losing out to Sheffield United in the play-offs.
This represents Vitek's third loan move away from United, following a successful stint with Blau-Weiss Linz in Austria, which ended in May.
The Czech Republic Under-20 international also had a spell with Accrington Stanley in 2024.