It has been released in a statement that "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".
Sir Terry leaves behind his three children and wife Lady Helen, as well as countless heartbroken friends who have taken to social media to express their sadness and condolences.
Stacey Solomon tweeted "So saddened to hear the news about Sir Terry Wogan, what an amazing man. So kind and talented. Thankyou for everything" after hearing the sad news about the 77-year-old star.
Sir Terry had a long career lasting 50 years within television and radio, during which time he presented his hit breakfast show Wake up to Wogan on BBC Radio 2 between 1993 and 2009.
He also helped to raised millions of pounds for charity Children in Need over the years. Lord Hall has said in a touching tribute to the star that "At the centre of Children in Need since its beginning, he raised hundreds of millions of pounds and changed so many lives for the better. He leaves a remarkable legacy."
BBC Radio 2 controller Bob Shennan also said: "As the host of Wake up to Wogan, Terry established himself as one of the greatest and most popular radio hosts this country has ever heard. We were brightened by his wonderful personality and charm as he woke us up every weekday morning, becoming an essential and much-loved part of our lives. "His millions of listeners adored him, as did his whole Radio 2 family. We will miss him enormously and our thoughts at this very sad time are with Helen and all the family. He leaves a remarkable legacy."
Jeremy Vine said: "He was probably the greatest broadcaster since the invention of the microphone. He lived for the red light and the sense that there was a listener at the end of the microphone. He only ever spoke to one person, because the greatest radio is intimate."
Graham Norton, who followed Sir Terry as Eurovision broadcaster tweeted: "He made it seem effortless and for a young boy in Ireland he made it seem possible. RIP Sir Terry Wogan."
Breakfast show host Chris Evans tweeted: "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."
Even Prime Minister David Cameron has taken to Twitter to express his sadness over the death of Sir Terry "My thoughts are with Terry Wogan's family. Britain has lost a huge talent - someone millions came to feel was their own special friend. I grew up listening to him on the radio and watching him on TV. His charm and wit always made me smile."
Our thoughts are with his family and friends at this sad time.