Robert Gillings, 63, of Addlestone, Surrey, was earlier convicted on two counts of indecently assaulting the girl, after a trial at Guildford Crown Court.
Ms Rantzen, television presenter and ChildLine campaigner, was not present at her house in the New Forest, Hampshire, at the time of the assault last August but had lent it to friends. Gillings, a former British Airways engineer, and his wife were invited by the girl's parents to visit them there.
The victim had told the court Gillings repeatedly assaulted her before the New Forest visit. 'He had said that if I told mummy he would kill her,' she said.
Questioned about the incident in the swimming pool, Gillings had told police: 'We were playing tag at the time, swimming backwards and forwards. It was just a bit of fun - my fingers caught hold of her bikini just at the bottom or the side somewhere.'
The jury returned majority verdicts of guilty on two charges of indecent assault, one of which took place at Ms Rantzen's house. They cleared him on two other charges.
Anne Cotcher, for the defence, told the court yesterday that Gillings refused to accept he was guilty. She said: 'This is not a man who . . . aimed to hoodwink the jury. He is sure in his own mind what's happened. He accepts, though, that the jury had taken a different view and he must be punished.'
Judge John Bull said the incident at Ms Rantzen's home was the culmination of a year of repeated assaults. Because both charges against Gillings were of a sexual nature against a five-year- old entrusted to him, he said only a custodial sentence would suffice.