The BBC confirmed his passing on Sunday (31 January), revealing that he had been battling cancer for a short time.
Many of his BBC colleagues, celebrity friends and his army of fans have been expressing their shock and sadness following the news, with many taking to Twitter to pay tribute.
Chris Evans, who took over the Radio 2 breakfast show from Terry in 2009, led the tributes, writing:
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.— Chris Evans (@achrisevans) January 31, 2016
Our most heartfelt thoughts go out to Helen, Mark, Alan, Katherine and Vanessa. To many of us Terry was Radio 2. We still can't believe it.— Chris Evans (@achrisevans) January 31, 2016
Fellow Radio 2 DJ Graham Norton, who also succeeded Terry as the British voice of the Eurovision Song Contest, also shared a touching message:
He made it seem effortless and for a young boy in Ireland he made it seem possible. RIP Sir Terry Wogan. I'll raise a glass during song 9.— graham norton (@grahnort) January 31, 2016
Jeremy Vine shared a lengthier post, writing:
Truly one of the greatest we have ever seen. And treated his colleagues like friends— Jeremy Vine (@theJeremyVine) January 31, 2016
“Sir Terry Wogan dies at 77” https://t.co/ClP1IC2Fpc
Many other tributes poured in for Terry, including:
No no no! In total shock. Goodbye my cheeky chum. Forever in our hearts. #RIPTerryWogan— Gaby Roslin (@GabyRoslin) January 31, 2016
Devastated about Terry Wogan. Grew up listening to him & have been privileged to know & work with him. Warm, generous & supremely talented— Clare Balding (@clarebalding) January 31, 2016
Sir Terry. Just the most warm hearted, generous, funny, clever, life affirming man. Part of the foundations of @BBCRadio2 so very sad.— Dermot O'Leary (@radioleary) January 31, 2016
Such a sad day today. The loss of such a legend...had the pleasure of being around such a warm welcoming person. Such a inspiration..— Rochelle Humes (@RochelleHumes) January 31, 2016
Listen to how Terry signed off his last Breakfast Show. His listeners were his friends and the bond was incredible. https://t.co/1tIg1pzXzv— Greg James (@gregjames) January 31, 2016
I'm so sad about Sir Terry Wogan. A radio talent like no other. So warm but so so funny. The best. RIP Terry— Scott Mills (@scott_mills) January 31, 2016
Terribly sad new about Terry Wogan . My thoughts are with his family. X RIP— Davina McCall (@ThisisDavina) January 31, 2016
He was THE BEST...A true gentleman and so very funny . Feel very sad . RIP Sir Terry x— caroline flack (@carolineflack1) January 31, 2016
He was a huge influence, watching his chat show, his genius commentary of Eurovision, warm & genuine interest in people & music. RIP Tel— edith bowman (@edibow) January 31, 2016
Prime Minister David Cameron also honoured Sir Terry on the social networking site:
1/2 My thoughts are with Terry Wogan's family. Britain has lost a huge talent - someone millions came to feel was their own special friend.— David Cameron (@David_Cameron) January 31, 2016
2/2 I grew up listening to him on the radio and watching him on tv. His charm and wit always made me smile.— David Cameron (@David_Cameron) January 31, 2016
BBC Radio 2, where Terry had been a DJ on-and-off since 1972, also aired a special tribute show on Sunday morning, hosted by Mark Goodier.
Sir Terry's family had confirmed news of his death in a short statement, which read: "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."
Back in November last year, Sir Terry pulled out of his long-time duty of presenting the BBC's Children in Need evening due to ill health.