Its maker, Piaggio Group, announced the museum project at a ceremony held at its plant near Pisa on Thursday.
The museum, which will open in a year's time, will house Piaggio's entire collection of the two-wheeler, including the first model, the Vespa 98, which careened down streets at 60km an hour.
Its latest three versions, the GTV, LXV, and GT60, revert to the original design. However, their engines are stronger and they pollute less.
The GT60, which pays homage to the first model, the Vespa 98 from 1946, is a limited series, with Piaggio making only 999 of them.
An affordable and sturdy means of transport for Italians recovering from the second world war, the Vespa was immortalised in 1953 when it carried Audrey Hepburn and Gregory Peck around the eternal city in the film Roman Holiday.
The Vespa became an international phenomenon, with lovers of its design and practicality joining clubs and becoming collectors.
Vespas have been sold in many
designs to attract young buyers
Demand was so strong that it only took 10 years for the one millionth Vespa to be sold in 1956.
At present, Piaggio estimates nearly 17 million Vespas have been sold since the first model rolled out of the factory.
Designed by aeronautical engineer Corradino D'Ascanio, it was called the Vespa, (wasp in Italian) for the buzzing sound of its small engine and its unusual looks.