Team Scotland's Ross Murdoch received the envelope, which contained drawings, after it was delivered to his parents' home, despite being addressed simply to ''Ross Murdoch, Commonwealth Champion, Balloch''.
The 20-year-old called on his Twitter followers to help him trace the youngster.
The young fan was later identified as Brian Fitzpatrick, from Dumbarton, West Dunbartonshire, and his mother said he will be "absolutely over the moon" to meet the 200m breaststroke Commonwealth champion.
Claire Fitzpatrick told BBC Radio Scotland's Good Morning Scotland programme that she thought her son was just "doodling" when he started on the letter.
She said: "We weren't sure that he would actually receive it and we thought he would get so much fan mail that we didn't give it much more thought after putting the stamp on it and posting it in the letter box.
"I didn't even know that he was actually planning to send it, I thought he was just doodling. He started school last week so he was practising and asking me, 'mum how do you spell I hope you like it', and 'how do you spell I'm your biggest fan', but I had no idea he was planning to send it at that point until he come up and asked for a stamp.
"I told him we had no idea of the address so we just thought, right, okay, we'll pop it in the post and see what happens."
Mrs Fitzpatrick's husband noticed Murdoch's appeal online and the family then tried to contact him via Twitter.
The Stirling University-based swimmer had earlier posted an appeal on the social networking site to try to trace the young fan.
On Twitter today he wrote: "Tks so much for your help in #FindingBrian! Delighted 2 have found him & look forward 2 meeting him soon @UofSSwim HQ."
He previously thanked Royal Mail for ensuring the letter reached him.
On August 11 he wrote: ''Parents received some fan mail today. Great @RoyalMail for getting it to the proper destination! Cute GoodJob''
Mrs Fitzpatrick said Brian loved watching Glasgow 2014.
"He loves swimming and has been going to lessons for the last year or so. I think it really caught his imagination when we told him about the races and the fact that Scottish athletes were competing (at the Games)."
On his meeting with his swimming hero, she added: "He will be absolutely over the moon."
Murdoch was one of the home stars of Glasgow 2014, winning gold in the 200m and bronze in the 100m breaststroke, and has since added two silver medals to his collection in the same events at the European Championships in Berlin.