Mr O'Neill, who rose to fame with his work with the Beatles and The Rolling Stones, died at home on Saturday following a long illness.
A spokesman for Iconic Images, which represents his impressive archive of photographic work, said: "It is with a heavy heart that Iconic Images announces the passing of Terence "Terry" O'Neill, CBE.
"Terry was a class act, quick witted and filled with charm.
"Anyone who was lucky enough to know or work with him can attest to his generosity and modesty.
"As one of the most iconic photographers of the last 60 years, his legendary pictures will forever remain imprinted in our memories as well as in our hearts and minds."
One of his last major public appearances was when he collected his CBE for services to photography from the Duke of Cambridge at Buckingham Palace in October.
After receiving his honour Mr O'Neill, who had been suffering from prostate cancer and was in a wheelchair, said the award "surpasses anything I've had happen to me in my life".
Actress and singer Barbra Streisand tweeted: "Terry O'Neill - You took such wonderful pictures. May you RIP"
Comedian and children's author David Walliams also paid tribute to the "genius" of Mr O'Neill, tweeting that his death is the "end of an era. RIP the great photographer Terry O'Neill. A huge talent and an absolute gentleman".
Mr O'Neill is one of the world's most collected photographers with work hanging in national art galleries and private collections worldwide.
His images have graced album covers, movie posters and magazine covers and by 1965 he was being asked to work with the biggest magazines and newspapers in the world.
The Royal Photographic Society said he had grasped that the youth culture of the 1960s was a key moment in time globally and he began to record the new faces in film, fashion and music who would go on to become megastars.
His work, which captures the heights of the Swinging Sixties, included The Beatles and The Rolling Stones when they were still struggling young bands, along with David Bowie, Led Zeppelin, Eric Clapton and Chuck Berry.
Film stars such as Sir Michael Caine and Raquel Welch remained lifelong friends. Sir Michael previously described Mr O'Neill as "a historian whose camera captured the resurgence and energy of this revolution".
He added: "I can think of no other photographer who has contributed so much to our heritage."
The Queen and former South African president Nelson Mandela have posed for portraits with Mr O'Neill and striking images of former prime minister Sir Winston Churchill are also among his archive.
Footballers Bobby Moore, Franz Beckenbauer, Pele and George Best; manager Brian Clough, boxer Muhammad Ali and Pakistani cricketer and politician Imran Khan were among the sporting greats whom he captured.
He was also known for his photographs of Audrey Hepburn, Elizabeth Taylor, Terence Stamp, Jean Shrimpton, Tom Jones, and Frank Sinatra through to singers Bruce Springsteen, Amy Winehouse and U2 in recent decades.
The Iconic Images spokesman said Mr O'Neill was also one of the first photographers to work with a new film franchise starring actor Sean Connery as James Bond.
He went on to work on several Bond films throughout the decades, including several with Sir Roger Moore.
Mr O'Neill, who was born in Heston, west London, had initially expected to become a priest but soon found his true calling to be music.
He set his heart set on becoming a jazz drummer and tried to get a job at an airline believing it would help him to travel to New York City and play in the jazz clubs. He opted for photography as a career when he could not find work as a steward.
He then got a life-changing lucky break while working for British Airways forerunner the British Overseas Airways Corporation.
He said: "Part of my work was to take photographs of people arriving and departing at the terminals. I happened upon a very well-dressed, bowler-hatted man taking a quick nap in the departures area, and he was surrounded by African chieftains, fully clad in their regalia.
"Soon after, I was approached by an editor who told me that they wanted to show the photo to his paper. The man napping turned out to be then-home secretary Rab Butler.
"The paper ran my photo and I was off and running. I was offered a job at the Daily Sketch where I worked for several years before going out on my own."