The scheme is the last of seven separate programmes, worth around £250 million in total, to enable the base to accommodate the new joint strike fighter jets, known as F-35s.
The contract for the work, which has been jointly awarded to Galliford Try and Lagan Construction Ltd, was announced by the Ministry of Defence on Wednesday.
North West Norfolk MP Sir Henry Bellingham said: “This is a massive vote of confidence both in RAF Marham and West Norfolk as a whole.
“Not only will it underpin and guarantee the future of the RAF’s most important airbase in the country, but the work will also create a very significant number of local jobs.”
The hangar will be able to accommodate 12 of the planes, which can also be deployed to Britain’s new range of aircraft carriers. Vertical landing pads will also be installed at the base.
Defence secretary Sir Michael Fallon said: “The F-35B aircraft will provide the UK with the ability to project our influence globally.
“This contract will ensure that RAF Marham has the facilities to match this world-class aircraft when it arrives next year.
“Throughout the F-35 programme, British firms have won major contracts creating thousands of jobs. The contract to improve the runways and taxiways as well as installing new landing pads will bring local jobs to Marham.”