Larkins, 19, played for the Hammers' Under-21 side last season and was regularly watched by O's goalkeeper coach Kevin Dearden.
He has signed a one-year deal, and Dearden told the club's official website: "Jake is someone that I've watched personally on a number of occasions and have been impressed with him.
"I had a good conversation with Martyn Margetson (the goalkeeper coach at West Ham) and he came highly recommended, so we got him in to train with us towards the end of the season and he did very well.
"The gaffer, Kev (Nugent) and I liked what we saw and we believe he will be a valuable member of the squad and be able to push Jamie (Jones) for a starting place straight away."
- Sports & Recreation
- Kevin Dearden
- Martyn Margetson