Molinari has enjoyed a remarkable season, winning his maiden major championship at the British Open along with his first Rolex Series title at the BMW PGA Championship.
Englishman Fleetwood, who needed to win at the Jumeirah Golf Estates to overtake Molinari in European Tour's money list, finished with a final-round four-under-par 68 to end 10-under overall, four shots off the current clubhouse target.
"It's incredible," Molinari said. "Now I'm going to have time to sit down and relax and really think back about the last few months.
"This morning on the first tee the announcement is the winner of The Open Championship, Race to Dubai leader, it does not sound real at the moment.
"It's more than I ever dreamed of achieving. I've seen guys that I think are better players than me not winning Majors and not winning Order of Merits or Race to Dubais. To achieve those things in one single season is just incredible."
Molinari was also part of Team Europe's Ryder Cup victory over the U.S. at Le Golf National in September, becoming the first European to win five points out of five.
Four of those points were won in a pairing with team mate Fleetwood.
"It's tough in a way because it would have been probably easier in a way to play against anyone else but him (Fleetwood)," Molinari added.
"I know how talented he is and I really thought at some point he was going to win it and put me in a tough spot.
"He's obviously a great guy and a super talented player and I'm sure being younger than me, he's going to win a few more Race to Dubais." (Reporting by Hardik Vyas in Bengaluru Editing by Toby Davis)