The Czech Republic forward impressed while on loan at Watford last season, scoring 22 goals.
West Brom boss Steve Clarke said: "I'm delighted to welcome Matej to the club.
"He had a really good year with Watford and we believe he's got the qualities to score goals at a higher level. Hopefully, he'll show that this year with us.
"We had Matej watched throughout last season. As well as some excellent scouting reports, we had some really good feedback from within Watford about Matej as both a player and person.
"I've said previously we're a bit light in the forward areas and Matej will increase competition for places. He's another good quality striker to add to the other three senior forwards we have here."