Mr Bennett, who was 82, was the first voice on Radio Ulster when it came on air in 1975.
In a broadcasting career spanning almost 60 years, he presented music, entertainment, sports and current affairs programmes.
His family said he passed away peacefully on Friday evening.
They said: “Our dad was a consummate professional, enjoying a long and celebrated career in broadcasting.
“In addition to this, he served many years as a teacher. He touched the lives of innumerable people, and they are ever the richer for his inspiration and influence.
“Northern Ireland has lost a lynchpin in local broadcasting. We, as a family, have lost a loving father, father-in-law and cherished granda.”
Famous famous from the broadcasting world paid moving tributes to a colleague they affectionately called “The President”.
Gloria Hunniford, who co-launched Radio Ulster with Mr Bennett, said she was “so saddened” by his passing.
“John was a giant in broadcasting. I have nothing but joyful memories of working with him,” she said.
“We had the privilege of launching BBC Radio Ulster together and we have been friends ever since.
“I loved him as a person, admired him as a broadcaster and have wonderful memories of him singing. He was a truly gifted, gracious and generous man.
“His contribution to audiences in Northern Ireland and beyond is immeasurable. He was a gentleman and great friend and I will miss him very much.”
Radio Ulster star Hugo Duncan described Mr Bennett as “a real gem”.
“I remember my very first day 26 years ago, coming into Broadcasting House full of nerves and one of the first people to put me at ease was John, who was the main morning presenter at the time,” he said.
“We shared so many laughs down the years and he even sang for me on the show. I’ll miss him and his friendship greatly.”
Colleague Lynette Fay said “everyone at Radio Ulster is heartbroken” at the news.
“He was full of chat, had a wicked sense of humour, and was so very kind. His listeners adored him, as did we,” she added.
Ralph McLean described Mr Bennett as “a true gentleman and the voice of Radio Ulster”.
“He was the best. Simple as that. He was so loved and respected by listeners and colleagues alike,” he said.
Fellow presenter Kerry McLean said she was “heartbroken that our lovely John Bennett has left us”. She described him as “such a sweetheart of a man and an absolute gentleman”.
Newsline presenter Declan Harvey said: “The president of the club has left us. We will never see his likes again, such an extraordinary range as a broadcaster. A kind and warm man. A pioneer, who showed the way.”
Colleague Tara Mills said he was “an absolute legend whose entire life was dedicated to radio and his listeners.”
Born in Belfast on July 12, 1942, Mr Bennett was educated at the Royal Belfast Academical Institution and Stranmillis College where he trained as a teacher, specialising in music. He then taught at Strandtown Primary School before joining the BBC.
Mr Bennett co-launched BBC Radio Ulster, with Gloria Hunniford, on New Year’s Eve in 1974.
He later became best-known as ‘The President’ of the weekend music programme The Sunday Club, which he presented for more than 44 years. Such was the programme’s popularity that it also developed to include a Saturday edition.
Mr Bennett had a life-long passion for music. He played guitar in a folk band and it was his love of the instrument which led to his career in broadcasting, following a studio session for the BBC.
He specialised in long-form interviews. With Bennett provided revealing insights into the lives of celebrities and his special Christmas morning programme, Calling Home, became another radio institution, connecting families at home and abroad for several decades.
Mr Bennett presented his own weekday morning show on Radio Ulster throughout the 1990s, combining music, current affairs and entertainment.
His passion for football made him a go-to commentator for hundreds of live matches on the BBC, including at Wembley Arena.
In January 2023, he was awarded an MBE for services to Television and Radio Broadcasting.
It was followed by his induction into the IMRO Radio Awards Hall of Fame. His citation noted that his career in radio had “left an indelible mark on the broadcasting landscape.”
Adam Smyth, Director of BBC NI, said: “John Bennett made radio presenting seem effortless.
“He didn’t just have listeners – he had followers. He was always in command of his subject matter, knew what connected with people, and when to keep himself out of it.
“John was with us from the very first day of Radio Ulster and has been an intrinsic part of the station ever since. It’s hard to imagine Radio Ulster without him.
“Our deepest condolences go to Siobhan, Mark and the whole family circle.”
Emma Dunseith, head of content production at BBC NI, said: “John was an exceptional broadcaster who made a very significant contribution to BBC Northern Ireland and BBC Radio Ulster.
“As one of Northern Ireland’s most recognisable voices, John presented with charm, wit and authenticity. He brought much needed companionship to listeners. John’s Saturday Club and Sunday Club were places of friendship, storytelling and music; commanding a legion of fans.”
Paul McClean, executive editor, said: “John was a special gent. A real one-off who could quote Shakespeare or Sinatra at the drop of a hat.
“His warmth and mischievous sense of humour filled the corridors of our station from its birth on New Year’s Eve 1974.
“We all admired and respected ‘The President’ and he will be greatly missed by all of our Radio Ulster family.”
Mr Bennett was married to Joan for 53 years, before she passed away in 2020.
He is survived by his daughter Siobhan and son Mark.