Jimmy Sainte, 29, who is a French national committed the offence at a flat in Charing Cross, Glasgow between November 1, 2007 and June 14, 2009 while he was babysitting.
His young victim, who is now 13, blurted out that Sainte had raped her while she and her friends were playing "telling secrets."
One of her friends told her mother who told a teacher who in turn told the head teacher who called in the police.
The young victim's mother told the High Court in Glasgow that when she she phoned Sainte and told him about the rape accusation he admitted it.
The woman, who cannot be named for legal reasons, said: "He told me it was the work of the devil."
In her evidence the young girl said: "He raped me up to twice a week for about a year."
She said she was too scared to tell any adults about the horrific abuse.
Sainte, whose address was given as Little Queen Street, Dartford Kent, was convicted of raping the girl.
He was cleared of a further charge of striking the girl with a belt and throwing a chair at her when it was withdrawn at the end of the prosecution case.
Sainte told police he was in Scotland on an extended holiday, visiting his uncle. Sainte arrived in the UK from from Nigeria.
Advocate depute Alison Di Rollo, prosecuting, said: 'The accused has no previous convictions."
Judge Lady Wolffe placed Sainte on the sex offenders' register and deferred sentence for background reports.
Lady Wolffe said: "This is clearly a very serious and anxious matter."
Sainte will be sentenced next month.
Defence advocate Lorraine Glancy will give her plea in mitigation then.