The Belgium international was one of the stand out performers in Ligue 1 last season, becoming hot property in the transfer market amongst some of the biggest sides in Europe.
His situation at Marseille has sparked even more attention surrounding interested suitors as Batshuayi announced that he would be leaving the club after he returns from the Euros in France, and the Hammers have taken the initiative early on to snap up the striker.
The deal was initially worth only £28.25m, however exchange rates are expected to fluctuate following the news that Britain shall be leaving the EU, putting a number of other transfers in major doubt.
The East London club are not the only side to take action in sealing the deal with the outgoing player, with Juventus reportedly tabling a lower offer to Marseille representatives, whilst Tottenham Hotspur are also looking to make a bid at some point this summer.
When asked about where his future lies beyond Marseille, Batshuayi insisted that no decision would be made until after the international tournament this summer, but admitted to admiring the Premier League: "I don't think about that, I prefer to concentrate 100 per cent on the Euros, then we will see what happens.
"Everybody likes the Premier League. It has a lot of spectacle, a lot of goals and many good players. It is natural that every good player is attracted by that league."
The 22-year-old endured a successful period last season, scoring 24 goals in Ligue 1, but appears to be looking for a new challenge away from Marseille, who finished 14 points off of champions Paris Saint-Germain last campaign.