Paul Moffat, 30, of Hopeman, Moray, began abusing the girl when she was just four years old.
At the High Court in Glasgow, he wept after he was found guilty of raping and sexually abusing the child between January 2014 and May 2015.
Moffat was remanded in custody by judge Lord Matthews and placed on the sex offenders register.
He will be sentenced next month.
Moffat denied the charges against him and claimed the girl was lying.
The court was told that searches of his computer and phone revealed searches had been made for "pre-teen sex", "Lolita" and "pre-teen underwear model".
Moffat denied that he had made the searches and claimed anyone could have accessed his phone or computer because they had no passwords on them.
The court heard that the offence came to light after the girl told staff at her nursery that Moffat had abused her.
Prosecutor Sheena Fraser said: "The police were called in and the girl then revealed more information to her mother about what Moffat had done."
The young girl did not have to give evidence in court.
The jury was shown a video interview of the girl's interview by police and social workers. They were then shown another recorded video of her being asked questions by defence advocate David Moggach.
Judge Lord Matthews told Moffat: "The jury has convicted you of a very serious offence."
After the verdict, he told the jury: "It was a relatively short case, but a particularly unpleasant one."
A man who raped a child was caught after his young victim told nursery staff she had been abused.