Sir Christopher, who acted as a pacemaker to help Sir Roger Bannister become the first man to break the four-minute mile barrier in 1954, died aged 82.
He died at around 7am yesterday at St John's Hospice in north west London having suffered from cancer for two and a half years, his son Mark Chataway said.
Mr Cameron said: "Chris was a rare politician in that he enjoyed such extensive, wide-ranging and successful careers both before and after he served in Parliament."
Sir Christopher won the first BBC Sports Personality of the Year in 1954 and later pursued a successful career in politics and business.
The Prime Minister said: "In politics, he held a number of influential positions and as the Government Minister responsible for introducing local commercial radio, left a lasting legacy millions continue to enjoy today.
"And after politics, Chris continued to hold senior positions with organisations as diverse as BT Systems, Laker Airways, and Bletchley Park. Chris was one of a kind; throwing himself into every project and achieving so much in so many fields. We have lost a great Briton, a true Conservative and a man of many talents.
"My thoughts and prayers are with Chris's family."
Mr Chataway, 53, called his father a "very compassionate and wise man" who had the "ability to put other people's needs first".
"We were, especially in these last few years, struck by his amazing qualities of humility and strength," he said. Mr Chataway said he and his siblings "grew up with him as a person, not as a runner", adding: "Of course we all thought it was remarkable. We all saw the old footage, but I think as a child that's not what you focus on in a parent."
Sir Christopher is best remembered for a race in Oxford on May 6 1954 which he did not even win. He was one of the pacemakers who helped Sir Roger Bannister become the first person to break the four-minute mile at the Iffley Road track.