The host of Channel 4's day time quiz show Countdown had been recovering from pneumonia and missed recording of the upcoming series.
The 61-year-old presenter from West Yorkshire fell ill back in May and was rushed to hospital in Bradford. He had been said to be "recovering slowly".
Whiteley, who fronted the show with Carol Vorderman since 1982, is still on screen as the show is pre-recorded.
Ms Vorderman's agent, John Miles, confirmed Whiteley had died.
Last November Whiteley was honoured with an OBE from the Queen, who is said to be a fan of the show, as was the late Queen Mother.