He was 77 and is survived by wife Rani and daughters Ritu and Tavishi.
Popularly known as Bhatia Sahib, the Delhi-based Bhatia ran in 5,000m and marathon events in Rome Olympics in 1960.
He was a contemporary of 'Flying Sikh' Milkha Singh.
Athletics Federation of India mourned the demise of Bhatia.
"Bhatia was a well known and respected figure in athletics circle not only in Delhi but throughout the country. His contribution to Indian athletics will always be remembered," the AFI said.
"I would call it passing of a legend," Milkha said.
"He was a perfect gentleman and a good athlete."
Recalling his days with Bhatia at Rome Olympics, Milkha said, "Even though Ranjit had come to Rome from Oxford where he was studying he met all of us warmly and we spent a lot of time together. We now have stopped producing scholar athletes.
Recalling his 800m race in Munich Olympic, Sriram said: "I had run a good race in Munich but the electronic board showed a very slow time against my name. Then Bhatia sahib protested on my behalf and it was found that a pigeon was stuck in the electronic wires of the board causing the machine to malfunction. Later the organisers corrected my timings."
After schooling at Lawrance School, Sanawar, Bhatia shifted to St Stephen's where he excelled in track and field.
Bhatia was awarded with Order of British Empire for his services to athletics and a being firm bridge between Indian and British sport.
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