Norwegian did not reveal how much they had paid for the aircraft, which can accommodate up to 20 percent more passengers over longer distances and with less fuel consumption than the Boeing 787-8 planes the company currently operates on its long-haul routes.
The new planes will be leased from New York-based company MG Aviation. This acquisition will bring Norwegian's Dreamliner fleet to 10 owned or leased aircraft.
The airline, which launched its long-haul business last summer, already operates three Dreamliners and the additional seven will be delivered by 2016.
Norwegian experienced serious technical problems with its first Dreamliners, from oxygen supply in cockpits to faulty hydraulic pumps and braking systems.
The incidents have affected the company's financial results, its share price and its image, but also the prestige of Boeing, which had invested heavily in resources and effort to bolster the new aircraft's market share.
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Boeing largely resolved the problems by sending technicians to Oslo, stocking spare parts at all airports where Norwegian operates and modifying the faulty aircraft.
"This is a fantastic airplane with high passenger comfort, long range and low fuel burn," Norwegian chief executive Bjørn Kjos said in a statement.