The construction period will be four and a half years and the contract is worth SEK1,140m (£99m).
“We are delighted to have been selected by the Norwegian Road Administration,” said Håkon Tjomsland, business area manager for NCC Construction Norway.
Building the new tunnel will shorten the journey along the E134 by about 11km. The contract also includes construction of 1.1km of roads on either side of the mountain, 5km of local roads and two crossings.
Work on the project will begin this year and is scheduled for completion in 2019.