Paul John's side became the fourth side to claim the Melrose Cup following in the footsteps of England, New Zealand and Fiji.
Wales put in a heroic performance against a side who have become one of the most consistent teams on the world sevens circuit.
Richie Pugh set Wales on the road to victory by scoring early in the first half before Argentina's Martin Rodriguez pounced on a Wales mistake racing 50 metres for a converted try and a two point lead but the inspirational Tal Selley reclaimed the lead for Wales with a smart individual try.
With Argentina trailing 12-7 at half time, Gonzalo Camacho levelled the scores with a well taken try and just when it seemed Argentina were upping the tempo, Thomas broke through the defence with a just over a minute to play to break the deadlock with a converted try.
Lee Beach was a proud Wales captain when lifting the trophy. "This is amazing, it's going to take a while to sink in," he said. "I can't describe it; the boys havve come a long way over the last three years. Things clicked in Wellington when we beat New Zealand and we continued that form here.
"When the going got tough in the semi against Samoa, we just said this is a semi-final of the world cup - that was motivation enough. And we did likewise in the final."
Paul John paid tribute to the entire squad who put in a massive effort throughout the tournament.
"This achievement is quite unbelievable. We've knew that when we beat New Zealand this morning, anything was possible. Our boys have been phenomenal and played some cracking sevens so it is thoroughly deserved. To beat New Zealand was great - it meant we had one big win under belt and fair play, the boys dug in deep and all the squad have been fantastic."
Wales were popular winners, acclaimed by a knowledgeable crowd who appreciate their sevens, and worthy champions after growing as a team, getting better and better through the rounds. Their brand of rugby succeeded but only because they had the right blend of players.
It was a historic night for Welsh rugby and one to savour.