Sir Terry Wogan has been hailed as a "national treasure" after his death from cancer aged 77.
The veteran broadcaster, known for his velvety voice on radio and television, was one of the UK and Ireland's best known stars.
A statement said Limerick-born Sir Terry died surrounded by his family after "a short but brave battle with cancer".
Leading figures in showbusiness and politics paid tribute to the much-loved star, with Prime Minister David Cameron saying he was "someone millions came to feel was their own special friend".
Sir Terry was last on air on BBC Radio 2 just under three months ago, on Sunday November 8, and days later was forced to pull out of presenting Children In Need at the last minute due to health issues.
A family statement issued by the BBC said: "Sir Terry Wogan died today after a short but brave battle with cancer. He passed away surrounded by his family. While we understand he will be missed by many, the family ask that their privacy is respected at this time."
Sir Terry, whose career spanned more than four decades, was known for his work on his BBC Radio 2 breakfast show, Children In Need, and the Eurovision Song Contest.
BBC director general Tony Hall described Sir Terry as a "national treasure", adding: "Today we've lost a wonderful friend. He was a lovely, lovely man and our thoughts are with his wife and family.
"For 50 years Sir Terry graced our screens and airwaves. His warmth, wit and geniality meant that for millions he was a part of the family."
He added: "For decades he's been such a huge part of the BBC on television and radio and leaves so many wonderful memories."
Prime Minister David Cameron tweeted: "My thoughts are with Terry Wogan's family. Britain has lost a huge talent - someone millions came to feel was their own special friend.
"I grew up listening to him on the radio and watching him on TV. His charm and wit always made me smile."
President of Ireland, Michael D Higgins, praised his "distinguished contribution" to TV and radio, adding: "His rise to the top of radio listenership in the United Kingdom was a great tribute to his breadth of knowledge and in particular his unique, very personal sense of humour."
Labour leader Jeremy Corbyn said he will be "missed by millions", while First Minister of Scotland Nicola Sturgeon said he was a "broadcasting institution".
Paying tribute to his friend, BBC broadcaster Jeremy Vine quoted a conversation between Sir Terry and the Queen, during which she asked him how long he had worked at the BBC.
Sir Terry replied: "Your Majesty, I've never worked here."
Broadcaster Tony Blackburn thanked Sir Terry for "being a friend", presenter Dermot O'Leary described him as "just the most warm-hearted, generous, funny, clever, life-affirming man", and Radio 2 DJ Chris Evans added: "We are all so terribly sad upon hearing of the passing of Terry. I can't put into words how the whole Radio 2 family is feeling."
Speaking outside BBC Broadcasting House on Sunday, Radio 2 DJ Simon Mayo told the Press Association: "I think people are shocked and stunned because of the fact that he was a radio genius. The staple of all great radio is the friend behind the microphone and he was the ultimate friend behind the microphone."
Despite Sir Terry's experience and great reputation Mayo, who first met him covering the 1992 Olympics, said he was the opposite of intimidating.
He said: "He was warm, funny, welcoming, generous. You would think 'oh my goodness, it's Sir Terry' and then as soon as you met him he'd offer you a biscuit and some cold curry that had been brought in the night before. I've worked with intimidating broadcasters and Terry wasn't that."
Piers Morgan hailed Sir Terry as "one of the greatest broadcasters who ever lived", and fellow Irishman Graham Norton said: "He made it seem effortless and for a young boy in Ireland he made it seem possible."
Pop star Sir Elton John posted a picture on Instagram of he and Sir Terry together from several decades ago, writing: "Such a special and funny man. A brilliant broadcaster and presenter. He came to our civil partnership celebration and was a loyal supporter. Love to his family. E xxxx."
Sir Terry lived for more than 40 years with his wife, Lady Helen, in the Buckinghamshire village of Taplow, where he was the patron of the Thames Valley Adventure Playground in Taplow, a centre for disabled children and adults, and once commentated on a celebrity cricket match for charity.
Nigel Smales, author of a history of the village, Taplow Moments - for which Sir Terry wrote the foreword - said: "This was a sanctuary to him and Helen in that he was a big, famous person but he came here to be private, and everybody respected that.
"While he had some very good friends and some slightly less well-known people like me, he was always very friendly, very convivial, always willing to talk and in fact just what you'd expect to see on television.
"He never flaunted his fame, he was just a really nice person, and we're all very sad to hear of his passing."
Among the floral tributes laid outside his home was one from Mark Jones, a neighbour and owner of the Wall Of Sounds record label.
He said: "He was just one of those legends of television and radio that you grew up with.
"He has always had that spirit of friendship."