According to Sky Sports News, a fee has been agreed between the two cubs with Sakho finally granted his wish of a move away from the Hammers.
The 26-year-old handed in a transfer request in July after West Ham reportedly rejected a £11 million bid from Sunderland for his services.
Sakho subsequently refused to travel with the West Ham squad for their pre-season tour of Austria.
Having shrugged off further interest from Sevilla and Hamburg, West Ham have seemingly agreed to offload the Senegal international to the Baggies – two years after he joined the club from French side Metz.
Sakho scored 12 goals in his first season at the London club, but failed to reproduce the same magic in the previous campaign with injury hindering his progress.