The statue will stand in Mayflower Park, overlooking the waterfront in the city where the plane was first built.
The 131ft (40m) replica will be one-and-a-half times the size of the actual plane and Solent Sky Museum hopes it will be erected in the next two years.
City council planners gave permission on Tuesday for it to be built.
Designer Nick Hancock beat more than 300 other people in a competition in 2010 with his entry showing a Spitfire on top of a mast that resembles a vapour trail.
Alan Jones, director of the museum behind the project, said: "It will be over £3m, but quite frankly that's got to be found - this is too important for Southampton not to be found.
"And I'm sure we will because there's tremendous interest, in fact across the world."
Mr Jones started the Solent Sky Museum 40 years ago as a tribute to RJ Mitchell and his Spitfire, which took off on its maiden flight in 1936 and played a crucial role in the Battle of Britain during World War Two.
It also tells the story of the wider aircraft industry between 1910 and 1960.
"This part of the world, this small geographical area of the Solent was the most important for aviation development and experimental work in the world," Mr Jones added.
"And the Spitfire of course was born and bred here."
Supporters of a new Spitfire memorial in Southampton have begun trying to raise more than £3m for the monument after it was given planning permission.