The 22-year-old follows Owen Evans through the door and arrives at Bescot having spent last season with League One side Wycombe Wanderers.
He has also been with the Baggies and Ipswich Town, taking in loan spells at Worcester City, Gloucester City, Rushall Olympic, Braintree Town, Concord Rangers and Chesterfield along the way.
"As soon as I spoke to the head coach it was appealing,” said Przybek, who has represented Wales at various age groups.
“He has big ambitions for the club and I get to move closer to home, so for me it was a no brainer.
“I am still young and I have got big ambitions in the game. For me, the move just made sense and hopefully it is the right step for me now.”
Przybek has three Wales Under-21 caps and played five times for Wycombe in all competitions last season.
Walsall chief Michael Flynn added: "We’re delighted to add Adam to the squad.
“He’s a Wales Under-21 international and has a bright future.
“He’s been at Ipswich; he’s been at Wycombe and both goalkeepers will provide each other with good competition.”