A spokesperson confirmed that Melinda died on Sunday morning at Cedars Sinai Hospital in Los Angeles, and was surrounded by her family, including her husband, at the time.
'Surrounded by her husband and loved ones, she passed away peacefully at Cedars Sinai Hospital in Los Angeles,' the statement read.
'Sir Tom and his family have asked for privacy at this difficult time and no further information is currently available.'
The sad news comes just days after Sir Tom cancelled his Asian tour 'due to a serious illness in his immediate family', pulling out of shows in Bangkok, Tokyo, Seoul and Osaka.
'He extends his deepest apologies to both the organisers and the fans, who he is most sad to disappoint,' his management said at the time.
Tom and Melinda married in March 1957, when they were both 16, when Melinda was expecting the couple's first and only child, a son named Mark. Tom revealed in interviews that he'd fallen in love with her even earlier, at the age of 12, and they remained married for 59 years.
Tom, Linda and Mark, pictured in 1971
In 2015, Tom told Sunday Times magazine that Linda, as he called her, had been experiencing depression, as well as prior cancer scares and loss of mobility, but their marriage remained strong throughout the struggles.
'I've realised she's had a depression since she was young,' he said.
'She's always had a touch of it. I don't think she really enjoyed getting out and about, and I think she was happy with being in the house.'
However, despite his hectic touring schedule, he added that the pair stayed in touch on the phone; conversations that were integral to their relationship.
'When you're face to face with somebody, you realise that time has gone on, but when you're on the phone we're both young again,' he explained. 'We haven't aged on the phone. You're not looking at one another, I'm looking at an old picture I carry around with me and leave by the bed. She says, "I don't look like that any more".'
'I say, "I know you don't, it brings back wonderful memories".'
'When we are on the phone, the whole thing, the depression, leaves her when we talk ... She is an unbelievable woman. She's the most important thing in my life. All the rest is just fun and games.' Our thoughts are with Tom and his family at this sad time.