The BBC reports that Mitchell, originally from Crumpsall, Manchester, collapsed while walking near his home in Stockport on Tuesday.
A family friend, Jo Houlcroft, confirmed the news.
"Pete collapsed whilst out walking near his home in Stockport, the cause of his death is still unknown but he was not thought to be displaying any signs of illness," Ms Houlcroft told BBC.
"He was knowledgeable and passionate about music of all genres, discovering and supporting many bands and was a huge part of the Manchester music scene.
"His wife Helen and two grown-up sons Adam and Sean are devastated by their loss."
Mitchell championed acts from his native Manchester across a 34-year career.
The 1990s saw IQ, his specialist weekend programme on Key 103, become an important platform for up-and-coming acts such as Oasis, 808 State and Happy Mondays.
Mitchell held posts at stations including Manchester’s Piccadilly Radio, Radio X and Absolute Radio, and was one half of the duo Pete And Geoff, with Geoff Lloyd, on Virgin Radio.
The Charlatans frontman Tim Burgess paid tribute to the presenter on Twitter, saying: "So sad to hear that Pete Mitchell has died. He was a friend of ours for thirty years.
Oh man, so sad to hear that Pete Mitchell has died. He was a friend of ours for thirty years. One of the first DJs to play and champion The Charlatans. Always a pleasure to catch up with him, such fond memories of our times together. My thoughts are with Pete’s family and friends pic.twitter.com/EAIrcSuzIa— Tim Burgess (@Tim_Burgess)March 13, 2020
"One of the first DJs to play and champion The Charlatans. Always a pleasure to catch up with him, such fond memories of our times together."
BBC Radio 6 presenter Chris Hawkins wrote: "Pete Mitchell was not only a brilliant and passionate DJ but he was a really honest bloke and a lovely, supportive person. He will be missed by so many."
In a statement on Twitter, BBC Radio 2 said: "We are saddened to hear of the passing of the much respected music radio presenter Pete Mitchell, who has worked on both BBC Radio 2 and 6 Music."
Content director for Virgin Radio UK, Mike Cass, said: “It’s incredibly difficult to think about Pete in the past tense.
“He was a great radio talent, a skilled interviewer, a true part of the Virgin Radio spirit and a wonderful man.”
A spokeswoman for the station said it would be broadcasting a tribute at a later date.
Additional reporting by Press Association.