His death was confirmed on Tuesday by a registrar at Maidenhead Town Hall, west of London, to the Press Association news agency.
Harris, who had a hit record with Tie Me Kangaroo Down, Sport, was adored by generations of children for his jovial on-screen persona and was so respected in the UK that he was once granted the rare privilege of painting a portrait of Queen Elizabeth II.
He performed with the Beatles and presented himself as the affable inventor of the novelty musical instrument, the wobble board.
But as his star faded, the veteran entertainer became one of the highest-profile celebrities to be embroiled in a massive British police investigation which followed revelations that the late BBC TV host Jimmy Savile had been a prolific child abuser.
In 2014, Harris was found guilty of 12 counts of assaulting four girls, some as young as seven or eight, between 1968 and 1986 and jailed for nearly six years, although one conviction was later overturned on appeal.
He faced further charges in 2017 but the jury was unable to reach verdicts and he was released from jail that year.
During the 2014 trial, the prosecution portrayed the bearded, bespectacled entertainer as a predator who groomed and abused one woman for her entire teenage and young-adult life.
Harris denied all the charges and said the allegations against him were "laughable".
The sentencing judge said he had shown no remorse for the harm he had caused.
Prosecutors said he had a "Jekyll and Hyde" personality who used his fame to exploit his victims.
Among the victims was a friend of Harris' daughter, who claimed he molested her when she was 13 to 19.
Harris had said their relationship was consensual, and his relatives and friends supported him throughout the trial.
But a jury convicted him of all charges, and a judge sentenced him to five years and nine months in prison.
Harris had enjoyed a 60-year career as a successful television presenter, songwriter and artist.
He was best known for his children's television shows such as Rolf's Cartoon Time and Animal Hospital, and had a number of hit songs in the 1960s.
With his relentlessly cheery persona, Harris toured and performed on TV for decades with his unusual act of rapid, performative painting - his catchphrase was "can you tell what it is yet?" - and singing children's songs like Jake the Peg.
Born in 1930, Harris grew up in a suburb of Perth, Australia, and was an award-winning swimmer as a teenager.
After several failed attempts at art school, Harris launched his television career with a slot on a BBC show in 1952.
As well as hosting children's shows, Harris was also known in the 1960s for performing popular songs including Two Little Boys, which became a No. 1 Christmas hit in the UK.
In 1993, his wobble board cover of Led Zeppelin's Stairway to Heaven also charted in the country.
By the 2000s, he was considered by many to be a national treasure of sorts: the Queen sat for a portrait painted by him in 2005 to mark her 80th birthday, and he starred in a concert celebrating the monarch's Diamond Jubilee outside Buckingham Palace in 2012.
After his conviction, the British Academy of Film and Television Arts, which had described Harris as "one of the world's most iconic entertainers," said it would withdraw his fellowship.
with Reuters
