From April 2018, the airline will offer daily services to Newark airport, and four a week to Boston Logan airport from May.
The airline said it will also announce two more trans-Atlantic routes from the new bases by the end of summer 2017.
Flights will be operated by new Airbus A321Neo aircraft and include a choice of two cabins, full-service premium and low-fare economy, free Wi-Fi and on-board charging points.
Primera Air will be the first airline for nine years to fly scheduled services to the USA from Stansted.
Andri Ingolfsson, president and chairman of Primera Air, said: "We are very proud to announce our new bases and routes to the US.
"With our brand new Airbus A321neo airplanes, we will operate routes traditionally served only by wide-body aircraft.
"Owing to unmatched efficiency of these new-generation aircraft, we will be able to offer unprecedented prices to passengers from France and the UK to the US.
"At the same time, we are very excited to offer a product and service concept that merges low fares and high quality - perfect both for leisure and business travellers."
Andrew Cowan, Stansted’s chief executive, added: “We’re thrilled Primera Air has chosen Stansted as its UK base for these exciting and innovative new long-haul services to the USA.
“We know from our customers that there is enormous demand for flights to New York and Boston from London and the east of England, so the arrival of Primera Air is fantastic news for both business and leisure passengers wanting great value, excellent service and the convenience of flying transatlantic from their local airport.”
Flights to both destinations go on sale on July 20 with prices starting from £149 one-way inclusive of all taxes, fees and charges.
Primera Air is a scheduled flight carrier operating flights to more than 70 airports in Europe. The airline is based in Denmark and Latvia, and is part of the Primera Travel Group, which runs travel agencies and tour operating companies in Sweden, Denmark, Norway, Finland, Iceland and Estonia.
Paris Charles de Gaulle has also been named as a new base.
