Mark Maclennan, 30, of Bath, was also found guilty of possessing and taking indecent images of children, something he had already admitted in court.
The boy, who was three, was raped at a nursery in the Lochaber area.
The girl was abused on numerous occasions in Stirling, Dunblane and Dunfermline.
He was also found guilty of having thousands of indecent images of children on a laptop that he donated to the nursery.
He should also have been found guilty of spectacular stupidity!
Maclennan was cleared of a charge of sexually abusing a girl at the nursery when she was aged between four and five. The jury found that charge against him not proven.
During the trial a taped interview with the boy was played to the jury.
In the video recording the three-year-old was questioned by police officers about the incident and said: "Don't like Mark."
The rape happened some time between 1 August 2012 and 23 May 2013.
The girl, who is now 19, said Maclennan touched her, on occasions, over a period of almost three years, including at a pantomime costume fitting. The abuse happened between October 2007 and July 2010.
Judge John Morris QC told Maclennan: "Given what you have been convicted of a prison sentence is almost inevitable." Almost!?? Almost!!!??? Are you kidding me?
He was remanded in custody and sentence was deferred until 27 February at the High Court in Edinburgh for background reports.
The jury of nine women and six men took 90 minutes to reach their verdicts.
Afterwards judge Morris told them: "This has been a very unpleasant case for all those involved."
The police inquiry into Maclennan was sparked after the boy told his mother of an incident at nursery. It later emerged it had been a rape.
The three-year-old's parents and friends cried and hugged as the verdict was given. I wouldn't celebrate yet; it sounds like Judge Morris may give him little more than a slap on the wrist.
I was informed today that Craig Hyslop is also currently on trial for a serious assault on a one year old girl. I can't find anything on the internet about it, but will keep checking. Hyslop is another nutcase who should be locked up for the rest of his life.