The Middlesbrough-born musician was diagnosed with pancreatic cancer and had his pancreas removed in 2001, and in 2016 he suffered a stroke.
Rea found fame in the late Seventies and Eighties with hits such as Fool (If You Think It's Over), Let's Dance and The Road To Hell.
A statement on behalf of his wife and two children said he had died in hospital on Friday after a short illness.
"It is with immense sadness that we announce the death of our beloved Chris," the statement read.
"He passed away peacefully in hospital earlier today following a short illness, surrounded by his family."
Rea's debut album titled Whatever Happened To Benny Santini?, a reference to the stage name his record label wanted him to adopt, was released in 1978.
The track Fool (If You Think It's Over) went on to be nominated for a Grammy.
He did not find such success again for a few years but by the time his eighth album On The Beach, spawning a hit single of the same name, was released, he was a star in the UK and around Europe, with sporadic hits in the US.
When Road To Hell was released in 1989, he became one of the biggest solo stars in the UK, and cemented himself as a favourite among a predominantly male audience of a certain age.
Two of his studio albums - The Road To Hell (1989) and Auberge (1991) - went to number one in the UK.
His most famous song, Driving Home For Christmas, first released in 1986, features in this year's M&S Food Christmas advert which sees comedian Dawn French sing along to the single in her car.
The track also features in a Christmas-themed album he released earlier this year which contains songs including Footsteps In The Snow and Joys Of Christmas.
Speaking about the song during the 2020 Mortimer And Whitehouse: Gone Fishing Christmas special, he told comedian Bob Mortimer: " I was on the dole when I wrote that.
"My manager had just left me. I'd just been banned from driving, right. My now wife, Joan, she had to drive down to London, picked me up in the Mini, and take me home, and that's when I wrote it."
Rea was good friends with Mortimer, who is also from Middlesbrough, and in 1997 they recorded Let's Dance for Middlesbrough Football Club's FA Cup final.
Paying tribute to the singer, Middlesbrough FC said in a post to X: "We're deeply saddened to learn of the passing of Chris Rea. A Teesside icon. Rest in peace, Chris."
Rea shared two daughters, Josephine and Julia, with his wife Joan, who he had been with since they met aged 16.
He credited his family with helping him to cope after his ill health.
"It's music and family with me. I'm only one of four, that's how I am. I'm 25 per cent of a unit. It's always been that way and we like it that way. In between that, there's music," Rea once said.
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