The Hammers have failed to score in their last three Premier League games, and are currently unable to call on record signing Andy Carroll, who remains side-lined with a foot injury.
Lukaku was allowed to leave Stamford Bridge on transfer deadline day, but it was Everton who won the race to secure his services.
The 20 year old impressed during a season-long loan spell with West Bromwich Albion last season, scoring seventeen goals in thirty-five league appearances.
He is set to make his debut for Roberto Martinez’s side this weekend, having missed the win over Chelsea last time out due to the conditions of this transfer.
Bet 365 make Lukaku the 6/1 favourite to open the scoring against West Ham, who welcome Everton to the Boleyn Ground this Saturday.