LONDON — John Surtees, who won the 1964 Formula One championship to become the only man to win world titles on two and four wheels, died Friday. He was 83.

The British driver’s family said in a statement that Mr. Surtees died after being treated for a respiratory condition.

Besides winning the F1 title for Ferrari, Mr. Surtees also won 500cc motorcycle world titles in 1956, ’58, ’59, and ’60.

‘‘We deeply mourn the loss of such an incredible, kind and loving man as well as celebrate his amazing life. He has set a very real example of someone who kept pushing himself at his peak and one who continued fighting until the very end,’’ the statement said.

Renowned for his courage and determination, Mr. Surtees will be remembered as one of the most gifted and versatile racers of all time.

He began his career on motorcycles in 1949 as a passenger for his father, a top sidecar racer, and went on to ride for Norton and MV Augusta. In addition to his four 500cc world titles he also won three at 350cc. He also became the first man to win the Senior TT on the Isle of Man for three years in succession.

He started more than 100 F1 grands prix, winning six, in a career that took him to Ferrari, Cooper, and Honda.

During the 1970s he also designed, built, and raced his own Team Surtees F1, F2, and F5000 cars.

‘‘He was a legend of the sport, a lovely guy who did so much,’’ three-time F1 champion Lewis Hamilton said. ‘‘It’s a shock to everyone.’’

Ferrari posted a black and white picture of Mr. Surtees posing next to team founder Enzo Ferrari on Twitter, with the message: ‘‘John Surtees, Motorsport legend and 1964 World Champion with Ferrari, passed away. Our thoughts are with his family.’’