The 22-year-old, who posted three second-place finishes last season as a rookie, ended the tournament 15-under 273 -- good for a one-shot victory over Britain's Chris Wood at Verdura Golf & Spa Resort.
Trailing Wood by a stroke at the par-five 14th hole, Olesen used a spectacular flop shot en route to a birdie, getting back to minus-15, while Wood carded a bogey on the hole.
The Dane then held on down the stretch to post the victory.
Sharing third at 12-under 276 were fellow Denmark native Soren Kjeldsen (68) and Nicolas Colsaerts (69).
Jose Manuel Lara registered a 4-under 68, earning the fifth spot at minus-11.
2014: The Year in Music [PHOTOS]