The Dane held his nerve on the last hole by carding the par he needed to finish a shot in front of Molinari, who was successful at the PGA Championship a week ago.
Entering the final day a shot off the lead, Olesen recorded seven birdies in a bogey-free 64 to finish on seven-under for the day and 22 under overall.
Molinari bogeyed on the penultimate hole to effectively cost him successive titles, while overnight leader Lee Slattery was third after a closing 67.
Elsewhere, Lee Westwood produced the joint-lowest round of the day with his six birdies and an eagle, seeing him finish in a share for fifth place with two others.
ITALIAN OPEN LEADERBOARD