Nineteen of the Russian's 21 championships have been achieved on hard surfaces
A revitalized Medvedev secured his initial trophy for 882 days with success over Frenchman Moutet in the tournament final.
The Russian, a ex- world number one, has endured a torrid season, managing just one match at the major tournaments and experiencing a difficult moment at the New York tournament.
Medvedev's inconsistency on the professional circuit - and issues with his serving in specific - caused him falling of the top ten and ultimately splitting with long-time mentor his previous coach.
Presently collaborating with his coach and Rohan Goetzke, Medvedev has consistently advanced in the past month - culminating in a closely contested competitive win over challenger Moutet.
It is Medvedev's initial trophy following the Rome competition and initial on a hard surface from spring of that year.
Victory also indicates he has won 21 titles at 21 distinct events.
"It's the first time I'm at a tournament with my children at once, so to get a title is really nice," said tennis professional the champion.
"This title is in dedication of my second daughter her name, because the initial championship I got when my first daughter my daughter was born was for her."
The tennis star, the 2021 US Open champion, had failed in his previous six title deciders, featuring in the German tournament previously this season.
Medvedev's counter-punching approach and frequent emotional displays on the playing surface had led observers to question if his skill to play at the elite level was over.
But the 29-year-old has altered his approach in recent weeks, making an effort to come to the net and compete positively, supported by an enhanced service.
He came back from a break down in the opening set against the difficult Moutet, winning four of the concluding five points to take the lead.
The competitors swapped breaks in the second set before the challenger, bidding for his initial ATP Tour victory, took control to push for a decider.
He defended four initial break points in a close final set before the champion broke to that score to serve for the match.
Appropriately, the winner clinched the title with a point at the net, with the Frenchman failing to handle a volley after two hours and 38 minutes.
