Aberg carded back-to-back rounds of nine-under 61 over the weekend at Sea Island to finish 29 under par, four shots clear of Canada's Mackenzie Hughes, who carded a 63 on Sunday.
The 24-year-old only joined the paid ranks in June, but won the final Ryder Cup qualifying event in Switzerland at the start of September and was hailed as a "generational talent" when given a wild card by Europe captain Luke Donald.
Aberg partnered Viktor Hovland to victory in the opening foursomes session in Rome and the same pair also thrashed world No.1 Scottie Scheffler and five-time major winner Brooks Koepka 9&7 on day two, a record margin for an 18-hole Ryder Cup match.
"I'm super happy. It's kind of beyond my dreams," Aberg told NBC after rounding off his maiden PGA Tour win with three birdies in the last four holes.
The victory will take Aberg into the world's top 50 and secure an invitation to next year's Masters at Augusta National, his first appearance in a major championship.
"It's really cool. To first off play on the PGA Tour, I have a lot of people to thank for that. It's been so much fun, six months that I'll never forget.
"This is what you dream of as a kid. This is the sport that I love and the sport that I'm going to love for a very long time. Watching these events from a very young age is what I've done so to see myself win is really cool.
"It validates my skillset and my capabilities. If you told me (I'd achieve) this a couple of months ago I would not have believed you. To be in this position I need to pinch myself in the arm.
"It's really awesome and I'm so happy for me and my team and all the people that are close to me."
Americans Tyler Duncan (65) and Eric Cole (67) tied for third, seven shots behind Aberg.
Aaron Baddeley posted a closing 69 to tie for 64th at eight under while fellow Australian Cameron Percy was tied 77th after a 68.
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