The former journalist, who was 90, died with his family around him on Friday lunchtime, a statement said.
Sir Bernard was a Fleet Street journalist before becoming a Government press officer, and served as Mrs Thatcher’s press secretary for all but the first few months of her premiership.
His family described him as a “journalist to his bones”, having started out as a reporter at the age of just 16, and continuing to file weekly columns to Express Online and The Yorkshire Post until a few days before he died.
Son John Ingham said: “To the wider world he is known as Margaret Thatcher’s chief press secretary, a formidable operator in the political and Whitehall jungles.
“But to me he was my dad – and a great dad at that. He was a fellow football fan and an adoring grandfather and great-grandfather. My family will miss him greatly.”
Born on June 21, 1932, and educated at Hebden Bridge Grammar School, Sir Bernard started his career in journalism aged 16 on his local paper The Hebden Bridge Times in West Yorkshire.
He worked with the Guardian before becoming a press officer for the Government, but positioned himself as a bitter enemy of “spin”, criticising those who practised the “black art”.
Sir Bernard went on to handle the media as Lady Thatcher’s press secretary while she served as Prime Minister. He was knighted in her resignation honours.
After leaving Downing Street, he wrote his memoirs, Kill The Messenger, about his life in No 10. He went on to work as a political pundit, an after-dinner speaker, a cruise lecturer and a newspaper columnist.
Sir Bernard was married to Nancy Ingham, a former policewoman, for 60 years. She died in 2017.
He leaves a son, two grandchildren and a great-grandchild.
John Ingham thanked his father’s nursing home, Tupwood Gate in Caterham, Surrey, and his previous in-home carers for their “wonderful care and support”.