According to Florian Plettenberg, the Bees have agreed a 20m (£17.2m) fee with Salzburg to land the 19-year-old on a "long-term contract" after completing his medical.
An announcement is imminent, with Schuster officially completing his switch to West London once the summer transfer window opens on Monday, 15 June.
The Austria Under-21 international has made 28 appearances for Salzburg this season, including a substitute outing in Champions League qualifying stage and several starts in the Europa League.
Schuster's European experience will come in handy if Brentford qualify for European competition this term. Keith Andrews' men are currently in the Premier League, two points behind seventh place Brighton & Hove Albion.
The Bees host Crystal Palace before travelling to Liverpool on the final day of the season. Two victories would surely guarantee a finish in Europe and give Schuster even more reason to feel excited about his move to England.