The Czech U-21 international has been allowed to leave the club after the Hammers brought in Manuel Almunia to provide cover for the injured Robert Green.
Stech had has limited first time opportunity since his arrival from Sparta Prague in 2006 and has spent time out on loan already with Wycombe Wanderers and Bournemouth.
In other goalkeeping news, 23-year-old Hungarian goalkeeper Peter Kurucz has returned training following 14months out with an anterior cruciate ligament injury.
Rob Green is expected to be out of action for another 4 weeks.