The orange P400 (one of just five ever made) can be seen racing across the stunning Gran San Bernardo alpine pass in northern Italy at the beginning of the film, as the as Matt Monro's 'On Days Like These' is played.
The classic car is then destroyed in a crash before being tossed off a cliff by a mafia gang.
But in real life, two separate cars were used during filming, with only one Miura being tossed off the cliff. The surviving Miura was discovered in Paris last year by two British businessmen.
Tyrrell, the founder and managing director of Cheshire Classic Cars, said they bought the long-lost car following a tip-off that it was being sold by an Italian businessman, Norbetto Ferretti.
He then flew to France and viewed the car in an underground car park in Paris, where Ferretti said the Miura was the one that had been used in the film.
Tyrrell used the car's serial number to officially confirm with Lamborghini, which was bought by Germany's Volkswagen in 1998, that the car had been leased by Paramount for use during the filming of The Italian Job.
“Each of these cars is unique,” Tyrrell added.
“They were all had stitched by Italian women, and so have their own 'fingerprint'. Forensic experts have reviewed high definition film stills and confirmed that the stitching in this car is identical to the one in the film.”
In spite of the car's age, it is still in mint condition and has just 19,000km on the clock.
The sleek two-door coupè has had just five owners in the last four decades and can still reach a top speed of 273 Km/ph.
Tyrrell with the iconic car. Photo: Cheshire Classic Cars
Tyrrell said that despite being a huge motoring enthusiast, the decision to sell the car came down to business.
“We're a classic car dealership and not classic car collectors, business comes first.”
There has already been a huge interest in the car, with some offers “well in excess of £1 million (€1.42m)”, Tyrrell said.
The discovery of the long-lost Miura, not to mention the offers on the table, have given Tyrrell, an ex-professional singer, cause to dust off his old microphone.
“I have actually re-recorded my own version of 'On days like these', which is now available to download from Amazon and I-Tunes. I'll of course be giving any proceeds to charity.”