Shorey joins the Baggies for an undisclosed fee after passing a medical on Monday.
“I’m delighted to welcome Nicky to the club,” manager Roberto Di Matteo told West Brom’s official website.
“He’s an experienced, solid, reliable left-back who likes to get forward and get involved.
“I also like the fact he’s English and knows what the Premier League is about. He’s a player I’ve liked for some time.
“I’ve very much signed Nicky to compete for the left-back position and I have some good options down that flank as Marek (Cech) can also play further forward.
“Nicky’s arrival will not only increase competition but also means we will have options should we suffer injuries or suspensions.”