Youssouf Mulumbu has joined West Brom from Paris Saint-Germain for £175,000.
Skysports.com broke news of the deal earlier this week and now the Baggies have confirmed an accord has been struck.
The 22-year-old joined the Baggies on loan in January and has put pen-to-paper on a one-year deal, with an option of a further year.
Mulumbu made a total of six appearances during last season after injuries disrupted his spell at the Hawthorns.
New boss Roberto Di Matteo said: "Youssouf didn't get an extended run last year due to his injuries but he did well when he was in the team.
"I saw him play for West Brom last season and I'm delighted he's now joined us on a permanent basis.
"He could be the player we're looking for in defensive midfield. He's still young and I'm sure he will get better the more games he plays for us."