The club says it will have more than 50,000 season ticket holders at the 60,000-capacity stadium, which was used at the London 2012 Olympics.
The Hammers are leaving the 35,000-capacity Boleyn Ground, more commonly known as Upton Park.
The final match at the stadium, against Manchester United, takes place on Tuesday evening.
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West Ham vice-chairman Karren Brady said: "[We] have always believed in the West Ham fanbase and knew we could fill the new stadium.
"Having made the bold decision to move to the former Olympic Stadium, we are delighted to see how it has captured the imagination of the Hammers fanbase."
Last month, it was confirmed that West Ham would pay £2.5m a season in rent, with the London Legacy Development Corporation also covering the running costs for the stadium.
West Ham have sold all of their season tickets for next season, when they move to the Olympic Stadium in east London.