The 22-year-old needed a par four at the final hole and after safely finding the green in regulation he took two putts from 30 feet to clinch the first prize of 166,660 euros at the Verdura Golf and Spa Resort.
Olesen's closing three-under-par 69 gave him a 15-under tally of 273 and a one-stroke win over Chris Wood of Britain (64).
Two shots further back on 276 in a tie for third place were Dane Soren Kjeldsen (68) and Belgian Nicolas Colsaerts (69).
"I'm still in shock," Olesen told Sky Sports. "I struggled early on with a bogey at the first but I'm really happy now.
"This means so much to me. My goal is to go all the way in this game.
"It will be tough because there are a lot of good players out here but this win is a big step in the right direction."
Victory on the picturesque seaside course near the town of Sciacca came as a relief to Olesen after he three times finished as a runner-up in his rookie campaign last season.
The Dane, a football fanatic who divides his loyalties between FC Copenhagen and Manchester United, returned five birdies and two bogeys to reach the turn in 33 - three under - on Sunday.
Olesen then offset a bogey five at the 13th with a brilliant birdie at the next hole.
He hit a wild second shot way left but recovered well by chipping on to the green and sinking his putt for a four.
Olesen was put under severe pressure in the last round by Wood after the Englishman carded seven birdies and an eagle in a best of the day 64.