Mr Barratt was best-known as the main presenter on Nationwide between 1969 and 1977, which often attracted an audience of more than 10 million viewers.
A family statement read: “We’re very sad to report that our lovely Dad/Husband/Mike/Michael Barratt died this morning. He was 94.
“He spent his final days being cared for at the wonderful Thames Hospice in Berkshire, surrounded by his family.
“A life lived to the full.”
A JustGiving page has been set up in his memory to raise money for the hospice.
Among those to pay tribute to him was broadcaster Simon McCoy. He wrote on Twitter: “Such sad news. The nicest of men who was interested in things going on in the world right up until the end.”
Last year, Yorkshire Post columnist David Behrens hailed Mr Barratt’s presenting skills on Nationwide following a pledge by new BBC director-general Tim Davie that the corporation would do more to better reflect life outside of London.
Mr Behrens wrote: “You have to be of a certain age to remember Michael Barratt fronting Nationwide on BBC1. It was his avuncular yet blunt Yorkshire presence that held together the daily technical shambles of trying to talk to a dozen regional presenters at the same time.
“It was The One Show of its day, except that it didn’t condescend. Viewers were still assumed to be at least as intelligent as the people in the studio.”
He added: “The first rule of showbusiness is to leave the public wanting more. That’s what Barratt did in 1977 when he stepped down from the helm of Nationwide.”