The Spaniard was expected to serve as back-up to Jussi Jaaskelainen after arriving in the capital, but he soon became first-choice under Sam Allardyce, and he is eager for similar success when the first ball is kicked in August.
"I am looking forward to what will be my second season at West Ham," Adrian told the club's official website. "We will be looking to work hard to have a strong season and will be trying to do our best from the start, against Tottenham in the first game at home.
"For myself, I have adapted and knowing the game here now more, I will be looking to add to my game and I am sure with any new arrivals to our team, this will make us stronger."
Adrian picked up three awards, including Signing of the Season, at West Ham's end-of-season awards evening.