Parfitt had suffered a series of health problems including having to undergo a quadruple heart bypass in 1997. In October, he said he would no longer be performing with his band after suffering from a heart attack in the summer.
In a statement on the band's website, Parfitt's manager Simon Porter said had been admitted to hospital on Thursday.
He said the family was "devastated" to announce the musician's death.
"He will be sorely missed by his family, friends, fellow band members, management, crew and his dedicated legion of fans from throughout the world, gained through 50 years of monumental success with Status Quo."
Parfitt is survived by his wife Lyndsay, their twins Tommy and Lily, and his adult children Rick Jnr and Harry, a statement from the family said.
Rick Jnr tweeted: "I cannot describe the sadness I feel right now. To many he was a rock star, to me he was simply 'Dad', and I loved him hugely. RIP Pappa Parf."
Drummer Jeff Rich, who played in Status Quo with Parfitt for 16 years, told the BBC he was "just a really good musician, very under-rated, great rhythm player", but his health problems were "a big issue for him".
He added: "When he had the last heart attack and he almost died a few months ago, I had a feeling that he wouldn't survive very long but in the back of your mind there's always this thing thinking maybe he's going to be alright now - but when I got the phone call, you know I was really upset."
Broadcaster Chris Tarrant, who knew Parfitt for more than 40 years, said: "I am truly shattered to have this news. We all honestly felt that he was getting strong again.
"Rick was the ultimate rock and roller. He lived and died as he wanted to... the world is a sadder and poorer place without him".
'Rocked our world'
Status Quo found global success with hits including Rockin' All Over The World and Whatever You Want.
Parfitt had been due to launch a solo career with an album and autobiography planned for 2017.
Queen guitarist Brian May tweeted: "Shocked and so sad to hear of the passing of Rick Parfitt. Hard to find words, You truly joyfully rocked our world. RIP dear buddy."
Peter Frampton said he was "so sad" to hear the news.
Meanwhile, Former Ultravox frontman Midge Ure wrote on Twitter: "Dreadfully sad. Lovely man. Thoughts go out to his family and friends."
Ure co-organised Live Aid in 1985, which was memorably opened by the Quo performing Rockin' All Over The World.
One of rock's most recognisable guitarists
By Nick Serpell, BBC obituary editor
With his flowing blond locks, denim gear and Fender Telecaster, Rick Parfitt was one of rock's most recognisable guitarists.
His partnership with Francis Rossi became the core of Status Quo, one of Britain's most enduring bands.
Their brand of boogie-woogie rock survived changes in musical fashion and made them one of the best-loved live acts of their generation.
As well as driving the Quo sound on stage, Parfitt penned many of the band's biggest hits.