Sir Christopher Chataway died at around 7am on Sunday at St John's Hospice in north west London having suffered from cancer for two and a half years, his son Mark Chataway said.
The athlete's interest in keeping fit stayed with him as his life progressed, and his son said that up until a couple of weeks ago he was on his exercise bike every morning.
Mr Chataway, 53, described his father as 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 kept his passion for running alive even when he was approaching 80 years of age.
"He kept running almost until the end of his life. He ran with a couple of my brothers in the Great North Run about three years ago now," Mr Chataway said.
Adding: "And then doing it in a very respectable time."
Mr Chataway said he believed Sir Christopher would like to be remembered as "a wonderful father, a husband, a grandfather".
"Those probably mattered more than any of the sporting or political things," he said.
Sir Christopher was also a Conservative politician and broadcaster.
He is survived by his sons Mark, Matthew, Adam, Charles, Ben, his daughter Joanna, his wife Carola and his former wife Anna.
Speaking about taking part in the Great North Run at almost 80-years-old, Sir Christopher said at the time: ''I sometimes think that running, which was a sort of tormentor in my youth, has returned to be a friendly codger in my old age - that what was Joe Stalin has turned into Dixon of Dock Green.''