The 25-year-old was a free agent after his contract expired at Racing Club, and he had been training with the Baggies after joining up with the squad for their pre-season tour in Sweden.
"I'm delighted to welcome Claudio to the club," boss Steve Clarke said.
"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."
The defensive midfielder has signed a three-year deal with an option for a third and will wear the number five shirt.
Having passed a medical, the deal awaits international clearance, which should be granted as he is understood to possess an EU passport.
Yacob had been at Racing for his whole career and captained the side since 2008. He made his Argentina debut last year and has scored one goal in three appearances so far.
West Brom have already signed Ben Foster and Yassine El Ghanassy this summer.