Bannister's family said that he died on Saturday in Oxford, the English city where the runner cracked the feat many had thought humanly impossible.
Bannister was diagnosed with Parkinson's Disease in 2011.
Bannister also won a European Championship gold medal that year but brought an end to his athletics career before the end of 1954 and went on to become a leading neurologist.
He practised his athletics in his spare time while studying for a medical degree at Oxford.
His effort would be bettered by Landy 46 days later, but Bannister's place in athletics folklore was secure.
Steve Ford, chief executive of Parkinson's United Kingdom said: "We're very saddened to hear of the death of Sir Roger Bannister". Bannister later wrote of the final moments of the race: "I felt at that moment that it was my chance to do one thing supremely well". Bannister burst through the tape in 3:58.8.
The current women's record for the mile, 4:12.56 run by Svetlana Masterkova of Russian Federation, is even longer standing, dating to 1996.
"I felt pretty exhausted at the end, but I knew that I would just about make it", he told reporters.
The 88-year-old passed away at home in Oxford after battling Parkinson's. The great legend I had an honor of meeting a few years ago.
Australian John Landy surpassed Bannister's record just a month later with a time of 3:57.9.
But the pinnacle of his sporting career coming on May 6, 1954 at Iffley Road sports ground in a race that was nearly canceled due to windy conditions. Sports Illustrated named him its first "Sportsman of the Year".
Echoing the sentiment of many who spent time in the presence of Bannister, Wendy Sly, Olympic 3000m silver medallist in 1984, said: "I feel privileged to have met a true pioneer in our sport".
"It was as much a psychological as it was a physical barrier and Bannister's success allowed mankind to enter a new world filled with possibilities", added Coe of a record that since 1999 has been held by Morocco's Hicham El Guerrouj with a time of 3:43.13.
In 2004, he was made an honorary freeman of the London Borough of Harrow, where he was born.
After completing his school education from the City of Bath Boys' School, Bannister continued his education in University College London, followed by Oxford University and St. Mary's Hospital Medical School. He won many mile and 800m races, and set his sights on the 1952 Helsinki Olympics.
- White House pushes back against report of McMaster departure
- Sky Sports pundit reveals shock name he wants to replace Arsene Wenger
- 7 things to look out for at this year's two meetings
- Avengers: Infinity War to release a week early in April
- United Nations rights council to hold urgent session on Syria's Eastern Ghouta
- REI Stops Selling 50 NRA-Linked Brands
- Pari is Anushka's best film ever, claims Virat Kohli
- Holi 2018: how to celebrate the festival of colour
- Saudi King shakes up military leadership
- MSU, Michigan to face each other in Big Ten Tournament