The Australian-born Harris, 93, had been seriously ill with neck cancer and had received 24-hour care, local media reported late last year.
Harris died peacefully surrounded by family and friends and has been laid to rest, his family said in a statement.
An artist and musician who first gained fame in the 1950s with the top 10 hit novelty song “Tie Me Kangaroo Down, Sport”, Harris went on to present primetime TV shows mostly aimed at children.
He performed with the Beatles, painted Queen Elizabeth’s portrait, and presented himself as the affable inventor of the novelty musical instrument known as the wobble board.
His song “Two Little Boys” spent six weeks at number one in the United Kingdom, the last chart-topper of the 1960s and the first of the 1970s. In 1993, his wobble board cover of Led Zeppelin’s “Stairway to Heaven” also charted in Britain.
But as his star faded, the veteran entertainer became one of the most high-profile celebrities to be embroiled in a massive British police investigation following revelations that the 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.
In 2015, Queen Elizabeth, whose portrait he once painted, stripped Harris of a royal honour she herself had awarded him. Australia also stripped him of numerous honours it had bestowed on Harris.
Rolf’s rise and fall
Born in Perth, Australia, in 1930, Harris was a prolific artist from childhood, given to silly noises and voices to mask shyness, a trait he said he learnt from his father.
He moved to London at 22 to attend art school with hopes of becoming a portrait painter like his grandfather. A year later, he got a job sketching cartoons on children’s television, work that continued through the 1950s while he performed nights, singing comedy songs with a piano accordion, in a club for Australian and New Zealander expatriates.
It was for that crowd in 1957 he wrote what would be his breakout hit, “Tie Me Kangaroo Down, Sport”, which he said was an attempt to localise Harry Belafonte’s calypso classic “The Jack-Ass Song”.
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”.
It was his embrace by the British establishment that finally brought his downfall. A woman who was assaulted by Harris decades earlier, when she was friends with his daughter, watched his televised 2012 performance at the Queen’s Diamond Jubilee Concert.
“That’s when I decided I wasn’t going to have any more of it” and would go to the police, she later testified.