Andrew Cairns, 36, of Robinson Street, Fulwood, Preston, was accused of seven counts of sexually touching the youngster in 2013 and 2014.
He was convicted of two of the charges, but acquitted of the other five.
The verdicts were returned following a trial at Preston Crown Court last week.
He will be sentenced next month.
Today the girl’s father, who cannot be identified for legal reasons, welcomed the convictions and said: “At least Cairns will be going to jail and that will give us some kind of closure after what has been an absolute nightmare for all the family.
“I’m disappointed that he wasn’t found guilty on all seven charges. And I’m also disgusted that because he denied it, my daughter had to go through the harrowing ordeal of going to court to give evidence against him.
“Since these offences happened, she has been scared to go out.
“She has been bullied because of all this and as a result she has been leading a sheltered life.
“It’s been horrible for her, but it’s also been horrible for my ex-wife and me seeing her suffer like that. It’s made all of us ill.
“I’m happy that he has been convicted and the judge said he is facing a jail sentence. Hopefully it will be a long one after what he did. He told my daughter no-one would believe her.”
Cairns will be sentenced on September 1.
He was granted conditional bail until then.