The 19-year-old defensive midfielder has signed on an initial three-year deal, with the option to extend for a further year.
“I am really looking forward to getting started here. It is a big thing,” the teenager said on West Ham’s official website.
“The under-23s and first team work closely, and I think that young players here have got a good chance of breaking through as they have done in the past.”
Elimby can also operate as a centre-back, and his versatility could boost his chances of breaking into the Hammers’ first team.