The company is looking to raise up to $250 million (£151.17 million) in the flotation.
The firm's revenues climbed 111 percent year-over-year to $124.2 million (£75.3 million) by the end of January 2014, up from $58.8 million (£35.6 million) the year prior.
According to the S-1 filing, Box had 21 million registered users as of January 31 and 34,000 companies paying to use the platform. It also had 972 employees at the end of January, up from 369 at the same point in 2012.
However, the company, founded in 2005 in California's Los Altos, has also been losing money over the last three years, with losses of $168.6 million (£102.2 million) in the year leading up to January 31 2014.
The losses can be largely attributed to the company's extensive sales and marketing efforts, which expanded from from $99.2 million (£60.1 million) for the year ending January 2013, to $171 million (£103.7 million) for the year ending January 31, 2014.
Co-founder Aaron Levie, aged 28, told Bloomberg in January 2013 that a Box IPO was on the horizon.
The cash that can be raised from an IPO will give Box the boost it needs in order to stay in operation while making the losses it has seen over the past few years.
Morgan Stanley, Credit Suisse and JPMorgan Chase are among the underwriters for the IPO.
Prior to today's announcement, Box was estimated to be worth between $1.2 billion (£730 million) and $3 billion (£1.82 billion), based on a Wall Street Journal assessment, last December.
Box opened its "international headquarters", in London's Mayfair area, last October, and today it is thought to accommodate over 100 Box employees working across sales and technical support.
Box opened its first office in London last June and claims to have doubled the number of users it has outside the US since then, partly as a result of strong demand from the Nordics, Benelux, Spain and Italy.
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