The 20-year-old's new deal will take him up to the end of next season, with an option to extend for a further year beyond that.
Potts failed to make a single Premier League appearance last term, but is hopeful he will soon feature more prominently in Sam Allardyce's future plans.
"I'm very excited to have signed the new contract," he told West Ham TV. "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."
