The 21-year-old is moving permanently to Juve.
Costa has signed a contract with the Bianconeri until 2029.
Juve have announced that they will pay Vitoria €12.5 million over four installments, plus bonuses of up to €2.5 million.
With Bremer and Juan Cabal out for the season due to injury, Juve have deployed Costa as ready-made cover.
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