Mulumbu, 22,joins the Baggies in a £175,00 deal. He spent the latter half of last season on loan at The Hawthorns.
"I saw him play for West Brom last season. He could be the player we're looking for in defensive midfield," said the Baggies manager Roberto Di Matteo.
"Youssouf didn't get an extended run last year because of his injuries but he did well when he was in the team. I'm delighted he's now joined us on a permanent basis. He's still young and I'm sure he'll get better the more games he plays for us."
Albion look set, however, to lose defender Paul Robinson after accepting a bid from Bolton Wanderers for the 30-year-old. They are believed to be asking for £1million.
The Newcastle United coach Chris Hughton said his side's week-long training base in the Republic of Ireland was a success after watching his side beat Shamrock Rovers 3-0 in their first friendly of pre-season.
"It was a nice way to finish off what has been an excellent week," he said. Hughton is in charge of the first-team as the club remains in limbo while chairman Mike Ashley seeks to offload it.