Smith's career began at hospital radio before joining BBC Radio 1 in 1975. In 1983, Smith took over the weekday lunchtime show and took on the Breakfast Show in 1986, succeeding Mike Read.
Mike founded Flying TV ten years ago and the company says his legacy will be FTV continuing to go from strength to strength."
Smith was a key figure in the early years of Comic Relief but largely stayed away from the limelight after a helicopter crash which injured both himself and Ms Greene in 1988. The qualified pilot and his then-girlfriend Ms Greene were injured when the helicopter he was piloting crashed in Gloucestershire.
Both passengers survived, although Ms Greene broke both legs and an arm, and Smith suffered a broken back and ankle. The Air Accidents Investigation Branch concluded that "... examination of the helicopter (including flight control, fuel, engine control, dynamic systems and the engine itself) revealed no failure or unserviceability that could have resulted in a loss of rotor speed".
More top news
Russia will pay the price for launching air strikes to prop up the Assad regime, the US defence secretary has warned.
'Vote Leave' - a cross-party campaign calling for Britain to leave the European Union in the forthcoming referendum - has been launched.
Sir Bruce Forsyth had to be rushed to hospital after a fall at his home.