Mark Ellis, 57, preyed on the 10-year-old during a series of attacks in 1991.
A jury at the High Court in Glasgow heard Ellis was running a football team and training school in South Lanarkshire at the time.
Ellis, who had denied the charges of lewd and libidinous behaviour, was remanded in custody and will be sentenced next month.
Ellis lived in Biggar at the time of the offences.
He later moved to the West Midlands and coached boys at Birmingham City.
The offences came to light after his victim, now 37, travelled to England to confront him.
Judge Johanna Johnston QC told Ellis: "You have been convicted of one of the most serious sexual offences... one against a child. It is a grave offence."
A former boys football coach has been found guilty of sexual offences involving a young player.