The 17-year-old defender has put pen-to-paper for the remainder of this season and the next three with The Hammers.
Cohen admitted to being surprised at receiving the contract and he hopes to make the most of the opportunity given to him by Alan Pardew's side.
"I wasn't expecting it to happen - it has come as a surprise, and it is obviously a good feeling," Cohen told the club's official website.
"It is strange because I thought I would just be playing for the Under-17s and Under-19s - so it is great.
"The hardest one to adjust to is probably from the reserves to the youth team, but you just do your best whichever team you play for.
"I wasn't sure if I would ever get to this stage, though obviously that is the aim and what you want."
Meanwhile, young Liverpool striker Steve Gillespie was handed a trial in West Ham's reserves this week.
