The Czech is well known to English football fans after a successful loan spell with Watford last season, and the 21-year-old will now get the chance to perform in the Premier League.
He scored 22 goals for Watford as they reached the Championship play-off final - a run which brought him to the attention of West Brom boss Steve Clarke.
"I'm delighted to welcome Matej to the club," Clarke said on the club's official website.
"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."
Vydra passed his medical this morning and will now link-up with his country for a friendly against Hungary before returning to England for Saturday's season opener against Southampton.
He is West Brom's third new signing of the summer following on from Nicolas Anelka and Diego Luego, while Goran Popov has also returned on loan from Dynamo Kiev.