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He was 77-years-old.
The BBC said the veteran Irish broadcaster's family confirmed he died after a short illness.
In a statement provided to The Guardian, his family 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."
Last year, Wogan celebrated 50 years in broadcasting.
He presented a weekly chatshow on Radio 2 and his career included leading the Eurovision Song Content commentary for more than 30 years, hosting gameshow "Blankety Blank," and BBC One chatshow "Wogan," which ran for a decade until 1992.
He was knighted in 2005.
BBC director general Tony Hall said: "Terry truly was a national treasure."
The BBC has published Sir Terry Wogan's obituary here.
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