The 22-year-old, who was named last season's Championship Player of the Year, was West Ham's primary target in his position under new boss Julen Lopetegui.
He has signed a five-year deal with the Premier League club with an option to extend for a further year.
Summerville said as cited by Sports Central: "I'm very happy, and I can't wait to get started. "It's the perfect next step for my career. West Ham United is a huge club, with lots of ambition and great players, so I'm really excited to be here and to get going. "I always try to follow my heart, and I had the feeling that this is the best place for me to continue developing as a player, and to push my potential as much as possible.
He added: "There is so much history here, and the team have done so well in the Premier League and in Europe over recent years. I spoke to the head coach, and he convinced me that I could make an impact, and help achieve success in the new season. "I think I'm here to help write more history here, and I'd love to help West Ham get back into Europe. I want to contribute lots of goals and assists, and I'm so excited to meet my team-mates and the fans, and get out there now."
The Dutchman scored 21 goals across 49 games in all competitions last season as Leeds missed out on promotion after defeat in the play-off final.
Summerville had entered the final two years of his Leeds contract and departs Elland Road after four years at the club.
The ex-Feyenoord forward becomes West Ham's fourth summer signing following the arrivals of defender Max Kilman, winger Luis Guilherme and goalkeeper Wes Foderingham.
Meanwhile, the Hammers have agreed a deal worth £27.5m including add-ons for Borussia Dortmund striker Niclas Fullkrug, while there is growing optimism West Ham can also strike a deal with Manchester United for right-back Aaron Wan-Bissaka.
.
