Surtees, 81, who won seven world motorbike championships before becoming F1 World Champion with Ferrari in 1964, has bought Buckmore Park in Kent.
Modern-day F1 champions Hamilton and Button honed their skills on the Chatham circuit.
Surtees and Buckmore Park announced the sale on their websites.
John Surtees Ltd, based in Edenbridge on the Kent/Surrey border, has bought the business and assets of Buckmore Park, but the circuit's former owner Bill Sisley is to stay on as a consultant.
Surtees, who lives in Lingfied, also runs the Henry Surtees Foundation, set up in memory of his 18-year-old racing driver son who died in a crash during a Formula Two race at Brands Hatch.
Henry, who began driving as a child at Buckmore Park, was a pupil at Worth School, West Sussex, when he died.
A series of fundraising events has been held at the kart circuit in his name.
Former Formula One world champion John Surtees has bought the karting track where Lewis Hamilton and Jenson Button practised as youngsters.