Nineteen of the Russian's twenty-one championships have been won on hard surfaces
A comeback the Russian player won his maiden trophy for nearly 30 months with a win over opponent Moutet in the tournament final.
Medvedev, a former number one, has endured a difficult period, winning just a single victory at the big events and experiencing a difficult moment at the New York tournament.
The player's varied form on the tennis tour - and difficulties with his serving in particular - resulted in him exiting of the elite rankings and ultimately splitting with long-time mentor Gilles Cervara.
Currently training with Johansson and Goetzke, Medvedev has steadily progressed in the past month - culminating in a closely contested three-set triumph over challenger Corentin Moutet.
This represents the player's first championship following the Rome competition and initial on a hardcourt after that period of that year.
Success also indicates Medvedev has won twenty-one titles at 21 distinct events.
"This marks the first occasion I'm at a competition with my children together, so to secure a title is particularly special," commented world number 14 the champion.
"This championship is in dedication of my child her name, because the initial championship I got when my child my daughter was delivered was for her."
The tennis star, the former major winner, had failed in his past six finals, comprising in Halle previously this season.
His retrieving play style and regular reactions on court had prompted observers to question if his ability to compete at the elite level was finished.
But the player has implemented adjustments in recent weeks, attempting to come to the net and perform positively, supported by an better serving game.
The champion recovered from a disadvantage in the first set against the tricky Frenchman, winning 4 of the concluding five games to gain the advantage.
The pair swapped break points in the second set before the challenger, bidding for his first ATP Tour victory, took control to force a third set.
Moutet rescued 4 early-game chances in a competitive final set before the Russian secured a break to 15 to close out the victory.
Suitably, he earned the title with a point at the net area, with his opponent failing to handle a return after a lengthy match.
