The 32-year-old has signed a two-year deal with the Baggies, becoming the third new arrival at The Hawthorns.
"I'm delighted to welcome Diego to the club," the Scottish coach told the club's official website. "He's an experienced centre-half who will increase competition in that area of the team.
"This is a tough league. You need as many good players in your squad as you can get – and Diego is undoubtedly one of those. Like some of the others we have here, Diego is another player who captains his country and is a leader.
"He has a real hunger and ambition to play and succeed in the Barclays Premier League and he will hopefully get a platform here to show everyone what he can do. However, Diego knows he's got a fight on his hands to get into the team.
Lugano joins West Brom from Paris Saint-Germain.