The 29-year-old arrives at the Hawthorns after two full seasons at the Stadium of Light, signing for an undisclosed transfer fee that surpasses the £6.5 million deal that brought Shane Long to the club in 2011.
Sessegnon had initially dismissed speculation of a move away from the club in July by confirming he was happy to stay in Paolo Di Canio's new-look Sunderland side.
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The moves comes as his former side announced a deal to bring Liverpool striker Fabio Borino and Andrea Dossena to the club on season-long loans, taking their summer dealings to 15 in what has been a radical overhaul of the squad.