The 25-year old, who has earned three caps for Argentina, joined the team in Malmo on Saturday for training and new manager Steve Clarke has moved quickly to snap up the midfielder onn a three-year contract.
"I'm delighted to welcome Claudio to the club," Clarke told the club's official website.
"He is an Argentina international with a real desire to prove himself in the Premier League and it's great to have him on board.
"Claudio's got different qualities to the other midfielders we've got at the club and he should complement the squad very well.
"It will take him a little bit of time to adjust to the demands of the English game and he's also got to learn our language, but we hope to have him up and running for the start of the season."
Yacob joined Racing Club in 2006, and has captained them since 2008, making 147 appearances before his contract expired.
West Brom's sporting & technical director Dan Ashworth believes that this signing is a coup for the Midland club.
"He's been a one-club man in Argentina up to now, having broken into Racing's first team at 17 and being appointed as their captain while still in his teens," Ashdown stated.
"To achieve that at Argentina's third or fourth biggest club, and then break into the national team with the wealth of talent his country have to choose from, is no mean feat.
"Claudio joins us with a great CV and is a terrific passer of the ball. He's a holding central midfielder who sits in front of the back four and controls the play.
"Claudio's also good at breaking things up. I believe he will be a great asset for us."