The agreement will provide customers with a broader route network and more choices, while also contributing to securing local jobs in Norway.
The regional carrier will continue to exist as a separate company with its own brand, organisation and headquarters in Bodo.
Wideroe covers more than 40 small and medium-sized airports across Norway, in addition to a few larger airports in Europe, while Norwegian offers more than 300 routes to 114 destinations in the Nordics and in Europe.
"This is a milestone in Norwegian aviation history," said Geir Karlsen, chief executive of Norwegian. "Our two airlines have existed side by side for many years and no one knows the aviation market in Norway better."
It comes after Norwegian tipped two million passengers in June ahead of an expected busy summer period for the airline.
"The tax level for air travel in Norway is particularly high, and this, in combination with fierce international competition, makes it difficult for a smaller regional airline to persevere without a strong partner," added Stein Nilsen, chief executive of Wideroe.
Both companies will continue to have bases and headquarters in Norway and employees will remain in their existing companies under existing collective agreements.
Norwegian will acquire Wideroe for a cash consideration of NOK 1,125 million (£82 million).