The DJ was known for championing acts from his native Manchester across his 30-year broadcasting career.
News of his death was confirmed by BBC Radio 2 with a statement on Twitter.
It read: “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.
“Our thoughts today are with Pete’s friends and family.”
Pete’s cause of death has not yet been confirmed.
Pete had previously presented on stations including Manchester’s Piccadilly Radio, Radio X and Absolute Radio.
He was also one half of the duo Pete And Geoff, with Geoff Lloyd, on Virgin Radio.
The Charlatans frontman Tim Burgess was among those paying tribute, remembering how he was “one of the first DJs to play and champion” his band.
“Always a pleasure to catch up with him, such fond memories of our times together,” he tweeted.
Pete’s fellow 6Music presenter Chris Hawkins said: “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.”