The 61-year-old, known for his loud ties and stripy jackets as much as for his homely manner on screen, had been suffering for some time with pneumonia.
He was rushed to intensive care in Bradford, West Yorkshire, in mid-May.
Mr Whiteley, from Ilkley, West Yorkshire, had presented Countdown since the quiz was first aired on Channel 4 when the station was launched in 1982.
The first programme to be shown on Channel Four when it launched in November 1982, Countdown outlasted every one of the station’s other programmes, bar the news.
The show was originally supposed to run for five weeks but now has regular viewing figures of four million and enjoys cult status.
Its genial, punning and bumbling host is believed to have clocked-up more hours on television screens - and more than 10,000 appearances - than anyone else alive, apart from the girl on the test card.
He presented the programme with maths expert Ms Vorderman and a popular feature of the show was his frequent anecdotes and puns often met by groans from fellow guests and audiences.
Mr Whiteley leaves behind a partner of 11 years, Kathryn Apanowicz, who shot to fame in EastEnders in the 1980s.
Mr Whiteley’s first foray into television began as a journalist on the local news programme Calendar on Yorkshire Television in July 1968.
He hung up his microphone in 1995 after a record 27 years as the news anchorman at Calendar.
In 1984 he was one of the first journalists at the scene of the Brighton bombing as he was at the seaside town’s Grand Hotel at the time it happened.
Another claim to fame was the feat of interviewing every Prime Minister since Harold Macmillan.
But he will always be associated with Countdown and dominated the afternoon air waves.
He never missed an episode in 23 years until he fell ill this year.
Channel 4 is currently filming a new series of the quiz, using celebrity guest presenters - all of whom have already appeared on the show.