TSG have accepted a €20m offer from Leeds for Stach.
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BBC Sport says Stach has also agreed personal terms over a four-year contract.
Stach stands at 6ft 4in and manager Daniel Farke is confident he can make an instant impact in the Premier League.
Leeds have also brought in defenders Sebastiaan Bornauw, Jaka Bijol and Gabriel Gudmundsson as well as midfielders Sean Longstaff and Lukas Nmecha.