The 77-year-old broadcaster has passed away after a short battle with cancer, his family confirmed on Sunday.
They said in a statement: "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."
BBC director general Tony Hall added: "Terry truly was a national treasure. Today we've lost a wonderful friend."
Terry was born in Limerick, Ireland and made his name on the national broadcaster RTE, first in radio and later as a TV presenter.
A number of celebrities have joined the President of Ireland and Britain's Prime Minister in expressing their sadness at the loss of the broadcasting legend.
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
Ireland's President Michael D. Higgins said in a statement: "I have heard with sadness of the death of Terry Wogan, one of the great figures of broadcasting.
So sad to hear the news about Sir Terry Wogan. So many amazing people lost to us this year. Can't wait for the day we destroy cancer.— Simon Cowell (@SimonCowell) January 31, 2016
"His was a distinguished contribution to television and in particular to the medium of radio.
"People in Ireland will remember his early career in Irish broadcasting. On his move to Britain his voice became one of the most often quoted, favorite radio voices.
"Always proud of his origins in Limerick, he made many returns to his native country for television and radio projects."
And Britain's Prime Minister David Cameron tweeted:
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
Last year he pulled out of hosting Children In Need for "health reasons."
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
It was the first time since the charity extravaganza launched in 1980 that he was not involved but he insisted he would be "watching, cheering and donating".
He said in a statement: "So here we are on the 36th edition of Children in Need, every one of which I've been proud to present since it started in 1980, and for the first time I won't be there to cheer you on with word and gesture to another record-breaking year.
"The British public, as always, will dig deep in their pockets and purses to help the country's disadvantaged children, knowing that every penny will go to those who need it most."
He is survived by his wife Helen, whom he married in 1965, four children and five grandchildren.