"Sir Terry Wogan died today after a short but brave battle with cancer. He passed away surrounded by his family," said a family statement.
Irish-born Wogan had a successful television career and hosted a hugely popular radio show for 27 years, retiring in 2009.
He offered commentary on the Eurovision Song Contest from 1980 until 2008, garnering a huge following with his light-hearted cynicism of the kitsch music competition.
Prime Minister David Cameron said Britain had lost a "huge talent".
"Britain has lost a huge talent - someone millions came to feel was their own special friend," he added.