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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 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.
Scores from the European PGA Tour Sicilian Open at the par-72 course on Sunday in Sciacca:
273 Thorbjorn Olesen (Denmark) 68 69 67 69 274 Chris Wood (Britain) 67 71 72 64 276 Soren Kjeldsen (Denmark) 65 72 71 68
Nicolas Colsaerts (Belgium) 67 71 69 69 277 Jose Manuel Lara (Spain) 69 70 70 68 278 Anthony Wall (Britain) 69 72 71 66
Shane Lowry (Ireland) 67 70 74 67
Andrew Parr (Canada) 71 69 67 71 279 Alvaro Velasco (Spain) 67 74 70 68
Estanislao Goya (Argentina) 65 73 72 69 280 Pelle Edberg (Sweden) 70 66 75 69
Rich Beem (U.S.) 69 69 73 69
Richard Green (Australia) 67 70 74 69
Tim Sluiter (Netherlands) 69 71 71 69
Tom Lewis (Britain) 68 73 70 69
Gareth Maybin (Britain) 68 73 70 69
John Daly (U.S.) 71 67 72 70
Graeme Storm (Britain) 68 73 69 70 281 Richie Ramsay (Britain) 71 69 76 65
Scott Jamieson (Britain) 68 73 74 66
Alex Haindl (South Africa) 66 74 74 67
Bernd Wiesberger (Austria) 67 71 75 68
Kim Si-Hwan (South Korea) 67 72 72 69
Scott Pinckney (U.S.) 69 70 70 72
Peter Lawrie (Ireland) 64 72 72 73
Lloyd Saltman (Britain) 71 68 69 73 282 Christian Cevaer (France) 69 71 74 68
Maarten Lafeber (Netherlands) 68 68 77 69
Victor Dubuisson (France) 71 67 75 69
Julien Guerrier (France) 68 69 73 72 283 Lloyd Kennedy (Britain) 70 71 75 67
James Morrison (Britain) 66 74 75 68
Richard McEvoy (Britain) 68 70 75 70
Ben Mannix (Britain) 72 68 73 70
Phillip Price (Britain) 70 70 71 72
Steve Webster (Britain) 70 71 68 74 284 David Lynn (Britain) 67 69 79 69
Shiv Kapur (India) 71 68 76 69
Matthew Baldwin (Britain) 70 71 71 72
Simon Wakefield (Britain) 69 67 74 74 285 Michael Jonzon (Sweden) 69 69 77 70
Alastair Forsyth (Britain) 67 72 76 70
Wil Besseling (Netherlands) 71 70 74 70
Victor Riu (France) 66 72 74 73
Craig Lee (Britain) 67 73 73 72
Garth Mulroy (South Africa) 70 67 74 74 286 Magnus Carlsson (Sweden) 70 69 77 70
Scott Strange (Australia) 70 69 77 70
Sam Hutsby (Britain) 67 70 78 71
Alessandro Tadini (Italy) 71 67 77 71
Andrea Maestroni (Italy) 69 71 75 71
Carlos Del Moral (Spain) 71 68 75 72
Gary Orr (Britain) 66 73 75 72 287 Kim Do-Hoon (South Korea) 68 71 79 69
Robert Coles (Britain) 69 69 80 69 288 Paul Broadhurst (Britain) 69 70 77 72
Richard Bland (Britain) 69 72 75 72
Joakim Lagergren (Sweden) 66 73 76 73
Jordi Garcia Del Moral (Spain) 68 72 75 73 289 Andrew Marshall (Britain) 71 70 76 72
Jose-Filipe Lima (Portugal) 73 68 75 73
Taco Remkes (Netherlands) 70 70 75 74 290 Jamie Donaldson (Britain) 65 71 80 74 293 Mikael Lundberg (Sweden) 69 70 77 77 294 Tjaart Van der Walt (South Africa) 69 70 81 74
