The BBC confirmed his passing on Sunday (31 January), revealing that he had been battling cancer for a short time.
Terry Wogan has died at the age of 77
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:
Fellow Radio 2 DJ Graham Norton, who also succeeded Terry as the British voice of the Eurovision Song Contest, also shared a touching message:
Jeremy Vine shared a lengthier post, writing:
Many other tributes poured in for Terry, including:
Prime Minister David Cameron also honoured Sir Terry on the social networking site:
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.