Bannister, who broke the four-minute barrier at Iffley Road in Oxford in 1954, passed away on Saturday after battling Parkinson's Disease in his later years.
He was "surrounded by his family who were as loved by him, as he was loved by them", the family said in a statement.
"None of my athletics was the greatest achievement", he said.
At St. Mary's Hospital Medical School, Bannister turned the focus of his athletic training to the four-minute mile.
"The world seemed to stand still, or did not exist", he wrote in his book, The First Four Minutes. It was as much of a psychological barrier as it was a physical barrier.
At the world indoor championships, the news cast a shadow over the final day of events on Sunday with the sell-out crowd in Arena Birmingham breaking into long applause after a special tribute to Bannister was screened.
"His achievement transcended sport, let alone athletics".
"His achievement was a moment in history that lifted the hearts of a nation and boosted the morale of a world still at a low ebb after the war".
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"We have all lost a giant and, for many of us, a deep and close friendship".
I'm so sorry to hear the sad news about Roger Bannister. It is often said that it was one of the greatest sporting achievements of the 20th century, so when you put it into that context, I think people start to understand it. He met with Sir Roger Bannister several times in the years before his death. "It is very hard to break records during Olympic competition, but winning races was better than holding world records".
But Bannister and Australian rival John Landy as well as others were threatening to break it. He was such a gentleman, so able to give encouragement to all the generations of athletes coming through and he'll be so sorely missed. What he did do, he left this massive, massive legacy.
Bannister was chairman of the Sports Council between 1971 and 1974, during which he developed the first test for anabolic steroids.
"He was a man of great distinction and honour in every sense. Rest in Peace Roger".
The condition progressively damages part of the brain over time and is one Bannister was familiar with, even before he was first diagnosed a few years ago, from his lengthy career as neurologist.
In 2015, the two-mile record was smashed by Mo Farah, who ran the distance in eight minutes 3.4 seconds, and this was his first world record. He told me the latter meant far more to him than the former.