The actor and TV presenter's manager Phil Dale said the star passed away in hospital surrounded by his family.
He was best known as the host of the famous children's show and for playing Detective Constable Scatliff in Z Cars.
Phil said: "It is with great sadness that the family announce that Geoffrey passed away in hospital with his wife, Sarah, and son, Tom, by his side.
"Geoffrey Hayes was an English television presenter and actor, best known as the host of Thames Television's top-rated children's show Rainbow, and for his portrayal of Detective Constable Scatliff in the successful TV Series Z Cars for the BBC.
"The family would like to express their thanks to the many fans over the years as it always gave Geoffrey so much pleasure to know that he and his Rainbow team had given so much fun to TV and theatre audiences over the years.
"There will be no further comment at the moment and it would be appreciated if the privacy of Geoffrey's family is respected at this most difficult time."
Hayes appeared alongside cuddly puppets Zippy, George and Bungle in more than 1,000 episodes of Rainbow from 1974 until 1992, having taken over from original host David Cook.
He played the long-suffering adult character, guardian and upholder of the peace in the hallucinogenic Rainbow house on the show, which aired several nights a week to children across the UK.
In 2002, Hayes, who struggled to find work after Rainbow was cancelled, said the secret to the programme's enduring popularity was that it was full of "magic, innocence and imagination".
He said: "Practically all the time people come up to me and it really breaks me up because they thank me for being part of their childhood. It makes me want to cry sometimes."
Hayes also had a recurring role in drama series Z Cars in the early 1970s, and appeared on programmes including Never Mind The Buzzcocks and Pointless Celebrities.
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