Sky Sports report that a club-record fee in the region of £16m has been agreed for The Irons' 26 year-old forward.
The move may now set a domino effect into action, with Saido Berahino now expected to make his long-awaited departure from The Hawthorns.
Sakho fee agreed
It has been a summer of speculation for Sakho having been linked with a move away from West Ham's new home of The Olympic Stadium all summer. It appears now that The Baggies have won the race to sign the Senegalese international.
After handing a transfer request in July, Sakho's reunion with former boss Sam Allardyce at Sunderland for £11m was rejected, with the Senegalese refusing to travel with Slaven Bilic's men on their pre-season tour of Austria.
West Brom registered their interest in Sakho earlier this month and have now moved to capture the striker, who has two years remaining on his contract.
Despite a disjointed campaign through injury and rotation, Sakho scored seven goals for The Hammers last term, including one on West Ham's swansong evening at The Boleyn Ground.
Senegalese move may see Berahino departure
Sakho arrival in the West Midlands may now see Saido Berahino get his wish to depart West Brom after a long and drawn out saga.
The 22 year-old has had a love-hate relationship with the club after chairman Jeremy Peace refused a deadline-day move away in January 2015. Berahino was dropped to the reserves and after another move away failed to materialise last summer, was again reduced to a substitutes role for the majority of last season.