Other destinations could include New York, San Francisco and Washington DC, with return fares starting from around £200.
The news came as Delta prepares to launch Edinburgh-New York flights tomorrow in competition with American and United.
Norwegian already flies to six Scandinavian and Spanish destinations from Edinburgh, and launched transatlantic flights from Gatwick two years ago.
Passengers are charged extra for check-in baggage, food and drink, and to reserve seats.
Chief executive Bjorn Kjos, speaking in Edinburgh yesterday, said: “We will set up a base at Edinburgh Airport and start to fly to the US from the spring of next year.
“It’s obvious people want to go there. We will start with a range of routes.
“We will definitely fly to Boston, and San Francisco and New York could be others.”
The airline said it had carried one million passengers from Edinburgh since launching flights to Oslo seven years ago
It has since added Copenhagen, Stockholm, Barcelona, Malaga and Tenerife. Mr Kjos said he plans more European routes from the capital.
However, he has no plans to fly from Glasgow – which has no routes to Scandinavia apart from Iceland – because Norwegian regards Edinburgh and Glasgow as “one area”.
Mr Kjos said its six Edinburgh routes were “only the beginning of our plans for expansion”.
He said: “Edinburgh will play an important role in our future UK growth and our long-term ambition is to deliver new, direct long-haul flights from Edinburgh.”
The airline chief said Norwegian might also launch Edinburgh-Gatwick flights to feed passengers to its other long-haul routes from the London airport if it won a second runway.
Aviation analyst John Strickland said Norwegian had successfully launched long-haul flights from Gatwick, but any plans to operate them year-round from Edinburgh could be tricky.
Mr Strickland, of JLS Consulting, said: “They may take passengers away from other airlines, including those flying indirectly via hubs like Heathrow and Amsterdam.
“But with low prices, Norwegian will grow the market by attracting more people to fly.
“The acid test will be if its flights operate year-round when demand is lower.”