The Daimler Super V8 LWB limousine, which features a specially designed handbag holder, was in royal ownership from 2001 to 2004.
It was sold by auction house Historics at Brooklands in Surrey, complete with its original documentation and photographs of the Queen driving it.
The car features a centre armrest which holds a sliding holder specifically designed for the Queen's handbag.
The buyer, Ian Lillicrap, said he had acquired a "little bit of history", adding that he had been "blown away by the fantastic condition it is in".
Auctioneer Fabian Hine said: "The new owner lives in Truro in Cornwall, so the car will stay in Britain.
"He is a collector of this type of vehicle. He also recently bought an Audi convertible which was used many years ago by Princess Diana.
"I think the new owner has still got quite a cheap motorcar.
"I think it will increase in value as the years go by, particularly if he doesn't do any more mileage."
The car's ashtray was designed to house the security lighting controls, including blue flashing strobes, flashing headlamps and flashing rear lights.
The limousine also features a pair of neon blue lights near the rear view mirror, which were used to identify the vehicle in which the Queen was travelling when approaching her destination.
The car, which has a four-litre engine, was sold with its original tyres, full-service history and original registration number.
The boot of the car contains fittings for a device allowing direct contact with the Home Office and Downing Street. The working parts have since been removed.
Sporting a British Racing Green livery, the car was tested over 2,500 pre-delivery miles before being handed over to the Queen.
A further 11,000 miles were covered while the car was with the Queen before the vehicle was returned in 2004 to the Jaguar Daimler Heritage Trust, with which it is still registered.
A car that was once owned and driven by the Queen has been sold for £40,500.