The news was confirmed by Judas Priest frontman Rob Halford, who shared a photo of Hinch, along with the caption 'RIP' on his Instagram story.
Hinch, who was born in Lichfield on June 19, 1947, played in numerous Birmingham rock groups, including The Pinch, the Generation, and the Bakerloo Blues Line, later Bakerloo.
He and Halford also played together in Hiroshima before they both joined Judas Priest in 1973.
Hinch played on Judas Priest's debut album, 1974's Rocka Rolla.
He left Priest the following year and pursued a career in management, working with several musicians, including Uli Jon Roth of Scorpions fame.
Hinch was married from July 1987 to April 2010 to Jane Dayus. They had a son, Fraser, who is a TV film director.
Hinch was taken ill on Wednesday, April 28, and passed away late afternoon on April 29.
In response to the news, former Judas Priest guitarist KK Downing - from West Bromwich - said: "I am extremely saddened to hear that John has passed away as he played his part so well in the creation and the history of Judas Priest.
"There are so many memories of crazy and fun times we all shared together.
"John was always so dependable and did everything to the best of his ability, including his drumming which looking back can only be described as faultless.
"The fact that he continued to play to his very last day is testimony to his ability and dedication to his love of the drums.
"I wish to give my sincere condolences to Johns family and loved ones from myself and all of you forever."
Meanwhile, the management and staff and Wolverhampton music venue KK' Steel Mill added: "Without the influence of people like John and all founder members of the great bands we love, the live music industry wouldn’t be what it is today.
"We are very sad to hear the news and of course send our best wishes to family and friends close to John.
Tributes and condolences are being shared across social media, with many posting pictures of the drummer with the caption 'RIP'.
One fan tweeted: "RIP John Hinch, founding member and drummer with Judas Priest.
"A fabulous drummer and a good friend."