The Iceland Under-21 defender has joined The Hammers following a successful trial spell and having left HK Kopavogur in his homeland, is now hoping to make a big impression in London.
"I am really happy to sign for West Ham," Eyjolfsson told the club's official website.
"I have heard of many good players that have come from the club's academy. When I was on trial in February I really enjoyed the tempo and style of training and it helped me take my talent to the next level.
"It is obviously very scary to move away from my family but it is my dream to play in England and what I have always wanted to do so that outweighs any apprehension I had about moving here."