Noble has become a regular in the Hammers reserves side since joining the club from Arsenal in January and is widely expected to make the step-up to first team level this coming season as West Ham aim to regain their Premiership status at the first attempt.
"I can confirm that David has signed and we are pleased about that," West Ham managing director Paul Aldridge told the club's official website.
"We look forward to him helping us achieve our aim of getting promotion at the first attempt."