Oates had worked for the BBC for more than 25 years, but had recently left to work as a freelance radio journalist.
The BBC said his death had come following a short illness, though other sources reported it as the result of a virus.
Oates worked primarily on football and rugby league, and was a noted Blackpool fan.
He had less than a year ago been commentating on the FA Cup match in which Bolton Wanderers midfielder Fabrice Muamba had suffered a near-fatal cardiac arrest.
“Everyone at BBC Radio Sport is in shock at this terrible news,” said Richard Burgess, head of radio sport at the BBC. “David was a trusted and much-loved colleague who provided many years of loyal service to the BBC.
"His enthusiasm for commentating and reporting on football and rugby league was boundless - we will all remember with great affection his love of Blackpool FC in particular. To lose him at such a relatively young age is a tragedy.”
Former footballer and now TalkSport radio host Stan Collymore added: “Sincere condolences to Lotty & Family at hearing the sad news of the death of David Oates.
“Worked with him many times, devastating news.”
“So shocked that BBC friend & colleague David Oates has died,” said Claire Balding. “He was a loveable Eeyore. Thinking of Lottie & the girls.”
"Blackpool FC would like to pass on its condolences to the family of BBC 5 Live broadcaster David Oates. Big Pool fan, will be sorely missed."
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- Death & Funeral