The Uruguayan defender has signed on loan until the end of the season with a view to making the move permanent after that.
"Williams comes highly recommended and is probably the best young player over in Uruguay at the moment. He has got into the last couple of Uruguayan squads," Baggies boss Bryan Robson has said of his latest aquisition.
"He is a tough tackler but he has also got very good technique and the reason I say that is when his team get a free-kick, he is the one who takes them.
"He is a hard type but he can pass the ball. He is a no nonsense centre-half which is what you usually get from Uruguay and Argentina.
"From what I've seen of him, he does have very good attributes. How long it will take him to settle down to Premiership football and the pace of the game, only time will tell.
"He is here on loan but with a view to a permanent deal in the summer if both parties are happy."