Sessegnon has been allowed to leave the Stadium of Light, despite manager Paolo Di Canio claiming last month that he did not want to sell the Benin international.
The playmaker had been linked with a move to Qatari side El Jaish, but has now secured a deal to stay in the Premier League.
Baggies boss Steve Clarke had been determined to improve his attacking options before the transfer window closed and will be pleased to get Sessegnon on board.
Clarke has also been linked with a move for Everton forward Victor Anichebe and an interest in bringing Chelsea striker Romelu Lukaku back to The Hawthorns on loan.
Earlier in the day, West Brom completed the loan signing of Morgan Amalfitano on loan from Marseille and the capture of goalkeeper Lee Camp on a short-term deal until January.