The contract is the largest in Skanska's history and follows the group also winning the contract to build the Metlife Stadium, where the American football teams New York Jets and New York Giants play.
The Skanska team, called LaGuardia Gateway Partners, was tapped by the Port Authority of New York and New Jersey to demolish the existing central LaGuardia terminal and build and maintain a replacement.
They beat out a competing bid by a team that included major rivals Aeroports de Paris, Goldman Sachs and the architecture firm Kohn Pedersen Fox.
Other members of the consortium are Walsh Construction, Vantage Airport Group, which manages nine airports around the world, Meridiam, Parsons Brinckerhoff, and HOK, the global architecture group.
Located in the borough of Queens, LaGuardia is one of three major airports serving the New York City region. Port Authority officials described the upgrade as necessary for New York to compete effectively with Tokyo and other global centers.
They said partners in the Skanska consortium have worked on more than 350 aviation and transport projects, including the John F. Kennedy Airport in New York and at international airports in Boston and Los Angeles.
Transport officials said the upgraded airport would replace a facility that currently suffers from overcrowding. Construction is scheduled to begin in the first quarter of 2016.
Several airlines fly between Sweden and New York, with budget carrier Norwegian launching a no-frills service in 2013.