The 20-year-old, whose deal also has the option of a further year, made two first-team appearances for the Hammers last season although they were both in cup matches.
Potts has made five league appearances for West Ham so far and he is now hoping to add to that tally next term.
He told his club’s official website: "I'm very excited to have signed the new contract. We're into the summer break now and it's good to put pen to paper.
"I'm looking forward to pre-season already and can't wait to get back going. Hopefully I can get a good pre-season under my belt and push into the season itself.
"It's going to be a massive year for me personally. Not only for the club, but also from my point of view it's a big year and I'm hoping to push on this pre-season and force my way into the team.
"If I can get into the manager's eyes, hopefully I can be in with a shout going into the first game of the season."