The news was announced in a Facebook post by his family.
A post on his official Facebook page said the rocker, who became a global star with hits like Bat Out Of Hell and I’d Do Anything For Love (But I Won’t Do That), died with his wife Deborah at his side,
It added that his daughters, Pearl and Amanda, “and close friends have been with him throughout the last 24 hours”.
The post said: “His amazing career spanned 6 decades that saw him sell over 100 million albums worldwide and star in over 65 movies, including Fight Club, Focus, Rocky Horror Picture Show and Wayne’s World Bat Out of Hell remains one of the top 10 selling albums of all time.
“We know how much he meant to so many of you and we truly appreciate all of the love and support as we move through this time of grief in losing such an inspiring artist and beautiful man. We thank you for your understanding of our need for privacy at this time.
“From his heart to your souls… don’t ever stop rocking!”
Meat Loaf, who was born Marvin Lee Aday but was also known as Michael, sold millions of albums worldwide, with the Bat Out Of Hell trilogy among his most popular musical offerings.
Hit single I’d Do Anything For Love (But I Won’t Do That) reached number one in 28 countries and earned him a Grammy award.
Besides music, his long career also included roles in a string of films such as Eddie in the 1975 musical film The Rocky Horror Picture Show, 1992’s Wayne’s World, and Fight Club in 1999.
In 2016 he was honoured with the Hero Award at the annual Q Awards ceremony, which he dedicated to everyday heroes and called on people to “bring love back into this world”.
The album Bat Out Of Hell was released in 1977 and was later adapted as a stage musical, which was written by long-time collaborator Jim Steinman and featured some of the musician’s best-loved hits.
American singer Cher and theatre boss Andrew Lloyd Webber were among those paying tribute following news of his death.
Cher tweeted that she had “so much fun” when she worked with him on his 1981 album Dead Ringer, while Lloyd Webber wrote: “The vaults of heaven will be ringing with rock. RIP Meatloaf. Give my best to Jim”, referring to Steinman who died last year.
Bat Out of Hell: The Musical announced that Friday night’s show at the New Wimbledon Theatre will be performed in his memory.
A statement said: “The company of Jim Steinman’s Bat Out Of Hell: The Musical here in the UK is deeply saddened to hear of the passing of their great friend and producer, Meat Loaf.
“He was with us when the show first launched in London at the Coliseum and in Manchester at the Opera House back in 2016 and then came to the show at the Dominion Theatre in London on 25 July 2018.”
It added: “The beat is yours forever.”
Meat Loaf had spoken openly about health issues that had plagued him, notably asthma, which caused him to collapse on stage during a concert in Pittsburgh in 2011, and in 2003 he was taken ill at Wembley Arena in London and was admitted to hospital.
Following an on-stage collapse in Canada in 2016, a statement issued at the time said it had been down to “severe dehydration”.
Meat Loaf initially made his name in theatre productions, including a Broadway run of Hair, and in 2012 he told the PA news agency about his roots as an actor.
He said: “I started as an actor, I am an actor. I started in New York in theatre, almost 10 years before Bat came out.
“While other people were playing out in bars and doing music, I was doing theatre, so that’s why Jim (Steinman) and I struggled so much because Jim and I both came from theatre, and they went ‘You’re not rock people. You’re theatre people. Theatre people don’t make records’. The public didn’t care, but I’ve gone up against that my entire career.”
His long music career saw him release more than 10 albums, with his final studio album, Braver Than We Are, released in 2012.
The singer regularly updated fans with messages on his Facebook page, saying in a post in November last year that he was planning to be back in the studio to record in January this year.
He wrote: “Yes, only 7 new songs but and a BIG BUT. Live tracks from (oh goodness I’m not that old) the 70’s great ones a great band and Jimmy on piano, the 80′ so many great live tracks in the 80’s great bands, the 90 and again a great band and so many great shows, 2000’s (how do you write that) great shows great band. Then Tracks up till I hurt my back(I have now had 4 back surgeries) The back surgeries hurt everything.”
He went on to detail operations he had undergone on his back, saying the “4th surgery Feb 2018 has left me in a lot of pain” and adding: “I now have 13 screws holding on a metal plate or plates in half my back.”
According to reports, he was also planning to launch a reality TV show based I’d Do Anything For Love (But I Won’t Do That), with American outlet Deadline saying in March last year that it was to be “a relationship competition series”.