She died at the Cedars-Sinai hospital in Los Angeles on Sunday, surrounded by her husband and loved ones, a statement said.
The former Voice coach and Lady Linda, as she was nicknamed, were childhood sweethearts and had been married since 1957.
He recently cancelled a number of his tour dates in Japan, Thailand, South Korea and the United Arab Emirates.
A statement said it was due to “serious illness in his immediate family”, adding: “He extends his deepest apologies to both the organisers and the fans, who he is most sad to disappoint.”
The couple had known each other since they were 12, and were both the children of coal miners in South Wales.
They started dating at the age of 15, and married a year later when they were both 16 in 1957. That same year, their son Mark was born.
In his 2015 autobiography titled Over The Top And Back, Sir Tom revealed they wanted more children, but a miscarriage had left Lady Linda infertile.
While promoting the book last year, the What’s New Pussycat singer addressed criticism about not including anything on his alleged affairs in the book.
He told American TV host Larry King: “I don’t think it’s important. It’s not what has made me. I’ve always looked at entertainers as ‘why is that person where he or she is?’
One of his reported long-term liaisons was with Mary Wilson of The Supremes, who published details of their tryst in her book, Dreamgirl: My Life As A Supreme.
Sir Tom said last year in an interview with The Sunday Times Magazine that his wife suffered from depression. He said: “I’ve realised she’s had depression since she was young. She’s always had a touch of it.”
The singer said that Linda had “lost her spark’’ and had let herself go, but added that their marriage was ‘’rock-solid’’ and said ‘’all the rest was fun and games’’.
In the same interview, he recalled his wife once beating him up at their home in Los Angeles after the story of an affair with a Miss World hit the tabloids.
He said: ‘’I stood there and took it. She chinned me. She punched and shouted.’’