The 18-year-old goalkeeper is expected to perform understudy duties to first-choice stopper Robert Green.
Stech has spent the last two years with the Hammers' youth academy, but manager Alan Curbishley feels he is ready to make the step up into the first-team fold.
"Marek has joined the club's pre-season training and will have the possibility of fighting for the back-up goalkeeping position," the player's agent Martin Riha told STK.
He is a regular for the Czech U19 side, but will miss the upcoming European Championships at that level as he has only recently recovered from a long-term injury.