The 29-year-old Brawn GP driver is the second owner of the 2008 all-black Veyron which has a top speed of 253mph – which makes it 33mph faster than his F1 car.
The supercar has covered just 1,500 miles and is for sale with Suffolk-based dealer Steve Hurn’s Specialist Cars for £899,995.
Its website states: “Bugatti Veryon 16.4, black/black leather interior, car comes complete with all usual refinements for a £1,000,000 supercar, fitted with sports seats, recently serviced by Bugatti, 2 owners 2nd being a Current Formula 1 driver car, can be authenticated, in absolutely stunning condition.”
Jeremy Clarkson reviewed the car on Top Gear and took part in a challenge against fellow presenters James May and Richard Hammond when he raced it from Alba, northern Italy to London while the two other stars travelled in a Cessna 182 aeroplane with Clarkson eventually winning out.
Clarkson declared the Veyron “the greatest piece of engineering ever. This is the greatest car ever made and the greatest car we will ever see in our lifetime”.
Button’s Veyron has an 8-litre W16 engine and four turbochargers and develops 1,001bhp and 922lb/ft of pulling power. This accelerates the hypercar from 0-62mph in 2.5 seconds.
The Somerset-born star is leading this season’s F1 championship with 70 points after winning six of the first seven races for the newly-formed Brawn GP team.
At the moment Button spends his time driving a Mercedes CLK DTM AMG, Ferrari Enzo, Audi RS6 Avant, BMW M5 and a Mercedes C63 AMG.
In the past Button has also owned a Ferrari F430 Spider, Ferrari 360, Ferrari 550 Maranello, Ford GT and Porsche Carrera GT.
The Brawn GP star is currently having a break in St Tropez after completing the gruelling Olympic-level Mazda London Triathlon, raising £17,000 for Make-A-Wish Foundation.
His next race for Brawn GP is the European Grand Prix in Valencia.