Police in Scotland had alerted forces across the UK to look out for the purple Nissan Skyline, which had the registration N40 SKY.
It was taken after a theft at a house in Livingston on Wednesday morning.
The car was said to be worth £47,000 and one of only about 20 of its kind in the UK.
Officers said they believed the car was immediately driven south and had been investigating reports of it being seen on the M6 in north west England in the early afternoon.
Police Scotland confirmed on Thursday evening that the car had been found in London with the assistance of the Metropolitan Police.
A spokesman said: "Enquiries are continuing into the associated housebreaking and officers are working to recover the other high-value items and cash which was stolen, and to bring those involved to justice."
A rare car that was stolen during a break-in at a house in which jewellery and cash worth more than £150,000 was also taken has been found in London.