• A statement from Sir Michael's family said: "After a brief illness Sir Michael Parkinson passed away peacefully at home last night in the company of his family.
• "The family request that they are given privacy and time to grieve."
Broadcaster Sir Michael Parkinson has died at the age of 88, his family has confirmed.
His TV career spanned seven decades, and he interviewed the world's biggest stars on his long-running chat show.
A statement from Sir Michael's family said: "After a brief illness Sir Michael Parkinson passed away peacefully at home last night in the company of his family.
"The family request that they are given privacy and time to grieve."
BBC director general Tim Davie led the tributes, describing Sir Michael as "truly one of a kind, an incredible broadcaster and journalist who will be hugely missed".
"Michael was the king of the chat show and he defined the format for all the presenters and shows that followed," Davie said.
"He interviewed the biggest stars of the 20th Century and did so in a way that enthralled the public. Michael was not only brilliant at asking questions, he was also a wonderful listener."
Radio 4 presenter Nick Robinson said: "He was the greatest interviewer of our age who owned Saturday night TV for year after year."
Comedian and broadcaster Stephen Fry described being interviewed by Sir Michael as "impossibly thrilling".
"The genius of Parky was that unlike most people (and most of his guests, me included) he was always 100% himself. On camera and off. 'Authentic' is the word I suppose."
Singer Elaine Paige added: "Such very sad news that Sir Michael Parkinson has died. Have known him for many years, sang on his TV chat show and attended many events with him.
"A legendary interviewer that will be remembered as the best of his profession. We will never see his like again."
Broadcaster and author Gyles Brandreth said Sir Michael's chat shows were "truly engaging conversations that brought out the best in his guests".
"And what an array of guests," he continued. "'Parky' was one of my heroes - and a lovely guy. A privilege to have known and worked with him."
Comic Dara O'Briain wrote: "I had the privilege of doing the Michael Parkinson show three times and it the most I ever felt like I was in 'proper showbiz'.
"He was a consummate pro on-screen, and generous and encouraging off-screen."
Sir Michael introduced the first Parkinson show in 1971 on BBC television. The show ran initially for 11 years and spanned hundreds of episodes in which Sir Michael combined an avuncular style with a journalistic background.
He returned to the BBC in 1998 for another run of the show. Sir Michael estimated he had interviewed more than 2,000 guests in total.
Sir Michael's high-profile guests included Sir Billy Connolly, Muhammad Ali, Sir Elton John, Madonna and Dame Helen Mirren. Of the many celebrities he interviewed, Sir Michael said Ali was his favourite.
Born in 1935 in the South Yorkshire village of Cudworth, Sir Michael was the son of a miner who instilled in his son a love of cricket.
He achieved two O-Levels and got a job collating sports results on a local newspaper.
After two years in the British army, he worked as a journalist for the Manchester Guardian (later renamed the Guardian) before joining the Daily Express in London.
He moved into television as a current affairs presenter and reporter for both Granada and the BBC before he was recruited to present his self-titled show on BBC One.
Sir Michael brought down the curtain on more than 30 years of his chat show in 2007 with a special two-hour final episode featuring David Beckham, Sir Michael Caine, Sir David Attenborough, Dame Judi Dench, Dame Edna Everage, Sir Billy Connolly, Peter Kay and Jamie Cullum.
Elsewhere, his TV career also included ITV's TV-am breakfast show, Give Us a Clue and BBC One's Going For a Song, while he had a three-year stint hosting Desert Island Discs on BBC Radio 4 in the 1980s.
Sir Michael also hosted a Sky Arts series called Michael Parkinson: Masterclass from 2012 to 2014.
He was made a CBE in 2000 and was knighted in 2008.
The presenter revealed he was receiving radiotherapy treatment for prostate cancer in 2013, and said he got the all-clear from doctors two years later.
Culture Secretary Lucy Frazer called Sir Michael a "broadcasting giant who set a gold standard for the television interview".
"He spent his life entertaining millions of us with his Saturday night talk show and was one of our most treasured TV personalities," she said. "My thoughts are with Michael's family and friends."
Yorkshire County Cricket Club said it would hold a minute's silence before play in York on Thursday "to show our respects" for Sir Michael.
Barnsley Football Club said it had "lost one of its favourite sons", adding the club was "deeply saddened" to hear of Sir Michael's death.
BBC One will re-broadcast a documentary, Parkinson at 50, on Thursday at 21:00 BST, in tribute to Sir Michael.