The Brough Superior 981cc SS100 was originally used in the 1930s.
The classic motorcycle cost £180 – the average annual salary at the time – when first bought.
The machine, which can still reach speeds of more than 100mph, today fetched £264,700 at auction.
The 87-year-old motorbike has been restored and was sitting in a private collection for more than half a century before being auctioned off.
It was originally used in the Scottish capital to help fight city crime.
The bike was one of two bought by police in April 1931.
The treasured item went under the hammer at Bonhams’ Spring Stafford Sale. It had been valued at £170,000 to £220,000.
The motorcycle had been originally advertised as “the ultimate” accessory for biker enthusiasts.
The buyer has not been named, having wished to remain anonymous.
The transation was carried out as part of the largest ever Bonhams Spring Stafford Sale of classic and collectors’ motorcycles taking place at the two-day International Classic MotorCycle Show.