Books of condolence have opened for Sir Terry Wogan, as his breakfast show successor Chris Evans paid tribute on air to "radio's Eric Morecambe".
The veteran broadcaster died of cancer on Sunday at the age of 77.
The books, in Sir Terry's birthplace of Limerick, will allow people to mark the passing of "a true son of Limerick", the city's mayor Liam Galvin said.
Evans told listeners of the BBC Radio 2 show that made Sir Terry's name: "He was the absolute governor."
A condolence book for Sir Terry has also been opened in the entrance of the BBC's New Broadcasting House in London.
In a career spanning 50 years, Sir Terry hosted TV chat shows, fronted the Eurovision Song Contest and was the face of Children in Need, while his long-running Radio 2 breakfast show regularly drew millions of listeners.
At the start of his breakfast show on Monday, Evans said: "He was radio's Eric Morecambe, Ronnie Barker, he was our Captain Mainwaring, our Basil Fawlty but he made us laugh every day for two hours and for over 30 years.
"All unscripted, all ad lib, always supremely assured, unwaveringly confident.
"And do you know why? Because he never took any of this seriously, least of all himself. He was the butt of most of his jokes.
"Laugh and the world laughs with you, sure, but Terry knew that if you go one better, and laugh at yourself then you're really onto something."
Evans described Sir Terry as his "radio dad" and said that Radio 2 was "in disbelief and shock".
"He taught me so much about being on the radio and not being on the radio," added Evans. "He was the absolute governor, everybody knows that."
BBC Radio 4 Today presenter John Humphrys also paid tribute on Monday's programme, calling Sir Terry "one of the greatest broadcasters of our age".
"Terry would be surprised by that description, at least, he'd affect to be. He liked to say that he never did anything, that required more than the minimal effort, and his success was down to 'natural laziness'. Which of course was complete rubbish," he said.
"You didn't get to be the consummate professional he was by being lazy. It's true that he had a few God-given advantages - he was charming and articulate and witty and quick-thinking and whimsical and subversive and sardonic and, well, the list is a very long one.
"But Terry had something else as well. He liked his audience, and they liked him. They felt he wasn't broadcasting to the nation, he was just talking to them."
Prime Minister David Cameron told Jeremy Vine's BBC Radio 2 show Sir Terry was a "wonderful human being".
"I remember growing up watching Blankety Blank and then the Eurovision Song Contest and he always made you smile, made you laugh. He had this fantastic sense of humour," he said.
Veteran broadcaster Sir Jimmy Young, who worked with Sir Terry on Radio 2, said he was "stunned" at the news and that his condolences were "very much with Helen and the family".
Sir Terry died surrounded by his family "after a short but brave battle with cancer", a statement released by his family said.
He leaves his wife, Helen, and their three children. The couple also had a daughter who died in infancy.
An online book of condolences will be hosted on Limerick's official website www.limerick.ie with separate books of condolence at council buildings in Dooradoyle and Merchants Quay opening on Monday morning.
The city's mayor said: "Despite his fame and the fact that he was based in the UK throughout much of his career, Sir Terry often returned home to Limerick and never missed an opportunity on radio or TV to speak about his Limerick roots.
"The council honoured him with the title of Freeman of Limerick in 2007, which I know was a title that meant very much to him and his family."
President of the Irish Republic Michael D Higgins has said Sir Terry was "always proud of his origins in Limerick", and returned frequently to his native country.
Family friend and broadcaster Henry Kelly added that he was "shocked" to hear of his death because Sir Terry had "put it out that he had a bad back".
The Game For A Laugh and Going For Gold presenter knew the Wogan family as he had been friends with Sir Terry's younger brother Brian when they were at Belvedere College in Dublin.
"I didn't know he was that seriously ill. I knew he'd been told not to do Children In Need because, as he quipped himself, they don't want an 'oul fella of 77 standing up for ten hours asking for money.
"For so many people in this country, it is going to be like a death in the family - they adored Wogan," he added.
Sir Terry had not been seen in public since November when he pulled out of hosting the annual Children in Need telethon.
Blessed with a warm wit and a surreal sense of humour, Sir Terry was one of the BBC's most beloved broadcasters. His career even included a brief stint in the charts with his 1978 cover of The Floral Dance.
He also provided the UK commentary for the annual Eurovision Song Contest for some 28 years, with many viewing his acerbic comments on the show as the highlight of the event.
From 1972 to 1984 he presented the breakfast show on Radio 2 as The Terry Wogan Show, returning after a decade away in 1993 to front the re-branded Wake Up To Wogan.
The second incarnation of the show regularly drew more than eight million listeners - dubbed TOGs, or "Terry's Old Geezers and Gals".
Tributes poured in as news of his death was revealed on Sunday.
BBC director general Lord Hall said: "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."
Radio 2 controller Bob Shennan said he was "one of the greatest and most popular radio hosts this country has ever heard".
Sir Terry began his career on Ireland's national broadcaster RTE as a newsreader and announcer, moving into light entertainment before joining the BBC, where he would stay for the rest of his career.
Radio 2 presenter Simon Mayo described him as a "radio genius", saying: "The staple of all great radio is the friend behind the microphone - and he was the ultimate friend behind the microphone."
Sir Elton John paid tribute to Sir Terry on his Instagram account.
The singer posted a picture of the two of them together, writing: "Such a special and funny man.
"A brilliant broadcaster and presenter. He came to our civil partnership celebration and was a loyal supporter."
Members of Sir Terry's BBC Radio 2 fan club Terry's Old Geezers and Gals (TOGs) have paid tribute to his work and commitment to charity.
Norman Macintosh, who organises the TOGs conventions, told BBC Breakfast: "He was the gentleman and the ultimate broadcaster.
"He talked to one person at a time and he felt like he was talking to you and he brought the whole audience into the show, and everyone felt like they were part of it."
Sir Terry announced his retirement from Wake Up to Wogan in September 2009, making his final regular appearance three months later.
When he broadcast at breakfast for the final time in 2009 he told listeners: "The years together with you have not only been a pleasure but a privilege. You have allowed me to share your lives with you.
"When you tell me how important I have been in your lives it's very moving. You have been every bit as important in mine."
Sir Terry, who continued to front a live Sunday morning show, last appeared on air on Radio 2 on 8 November 2015.
The One Show: A Tribute to Sir Terry will be broadcast at 19:00 GMT on Monday 1 February.