And that will trigger the departure of fellow striker Saido Berahino as Stoke and Crystal Palace battle for his services.
Sakho has agreed terms on a switch from West Ham to the Hawthorns and the fee for the 26-year-old
will eclipse the £12m Albion paid Zenit St Petersburg for Salomon Rondon 12 months ago.
Sakho, who was also being chased by Sunderland, hit double figures in the Premier League in his first season with West Ham after signing from French club Metz.
Saido Berahino - Spotlight on
But he managed just seven goals in total last season and asked to leave the Hammers earlier this summer after slipping down the pecking order under boss Slaven Bilic.
Sakho’s arrival at West Brom will allow them to finally cash in on
the unsettled Berahino, with Stoke favourites to land the England Under-21 international valued at around £20m.
West Brom manager Tony Pulis has long been resigned to losing Berahino.
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The 22-year-old wanted to leave last summer but was prevented from going to Tottenham after they refused to cough up the £25m asking price.
The fee this summer might not quite reach that level but, with two clubs interested and a replacement in the bag, Albion chairman Jeremy Peace still hopes to drive a hard bargain.
Pulis will be given the cash to spend as he also wants a new left-back, with Leicester’s Jeffrey Schlupp and Leeds’ Charlie Taylor on his hitless.