A heritage lottery grant of £9m and a £5m grant from BAE Systems, towards the £19.3m project, will be announced today.
The grant comes as part of a raft of awards being given to projects around the country, with the National History Museum emerging as one of the major beneficiaries.
Although private Spitfire owners still fly many of the handful of fragile survivors at the Duxford base, the 1947 Mark 24 Spitfire, the last supplied to the RAF, is the only one in the Imperial War Museum's collection.
It has been restored to its original condition, but will never fly again.
It will be one of the stars of a spectacular display of a remarkable collection of military and civilian planes that will be the largest aviation museum space in Europe, and one of the largest in the world.
The collection spans a century of aviation history, from the first world war planes, including the canvas-covered Bristol Fighter, and the RE8, the first reconaissance aircraft, to Concorde - the museum owns the pre-production model in which test flights were made.
The museum's Spitfire is at present displayed on the ground, but in the new display will be suspended from the ceiling as if in flight.
The museum will today announce details of Air Space, which will be created inside an undistinguished but vast aircraft hanger, built for the museum in the 1980s to get as much as possible of the collection safely under cover, including exceptionally rare planes like the Sunderland flying boat.
Although the hangar had public access, its displays were rudimentary and had no temperature or humidity control.
The new display will create more than 7,750 square metres of floor space and half as much again by suspending aircraft from the roof. It is expected to hold 26 of the most valuable of the 180 planes in the museum's collection.
The display will for the first time match the military planes with their civilian counterparts.
The display will include a few spectacular failures, including TSR2, a revolutionary design of the early 1960s which would have put Britain far ahead in the international air race, until it was scrapped by a government faced with soaring costs. There are still a few surprising gaps in the collection, which Duxford director Ted Inman would like to see filled: if the RAF, or some friendly millionaire, would like to donate a 1980s Tornado, or the current Jaguar fighter, they would be welcomed.
The grant is the second lottery windfall for Duxford, which won a grant six years ago to build Lord Foster's award winning design of the American Air Hall.
The Duxford grant is among almost £40m worth of museum and gallery allocations, or grant agreements in principle, to be announced today by the heritage lottery fund. The Natural History Museum is to receive £14.9m plus £600,000 development funding for the Darwin Centre, which will provide a home for its 6m pressed plants and 28m insects as part of a rejuvenation plan.
The funds will also go towards the provision of laboratories for 125 scientists and to enable the public to enjoy increased access to material collected on the travels of Captain Cook and Charles Darwin.