Cameron MacGregor, 18 and from Uphall, took a punt on Japan potentially reaching the quarter-finals of the Rugby World Cup when placing bets on the competition in February.
He was offered 150/1 odds, the same as the odds Japan were given to win the full competition in September.
A month later following Japan's quarter-final clinching victory over Scotland, Cameron and mum Jill went back to the shop to collect their winnings, only for the shop assistant to refuse to pay out.
Instead of paying out the £1,500 winnings on the original bet, the family were told that they had been given the wrong odds when making the original bet and were told the shop would only to pay out on 20/1 odds, leaving Cameron £1,300 out of pocket.
A spokesman for William Hill said: "We are paying out the bet in full and it was a human error on our part."
The news they would receive their rightful cash was met with joy by mum Jill.
She said: "Oh my god thank you so much, the power of the press! We are delighted and many thanks to the Evening News.
"We are delighted, I get it was human error but it was their error not ours, so the bet should have been honoured from the beginning."
Cameron is planning on buying a personalised number plate with the winnings.
The news came after a week of disappointment for the MacGregors who had felt wronged by the decision not to honour the bet.
"The shopping assistant had written out the betting slip very clearly,“ said Mrs MacGregor. "It was then authorised with date and time and handed to my son.
"Last Sunday, we cheered Scotland and Japan with divided loyalties and when Japan won my son was delighted.
"On Tuesday we handed over the slip and the assistant said she would have to phone her boss. We were then told the odds given were incorrect and they offered us 20/1."
She said: "My son is not a gambler. He put a fun bet on the Rugby World Cup as he loves rugby. My son felt cheated."
However she was delighted that William Hill had decided to pay out the winnings in full.