Nineteen of the Russian's 21 championships have been earned on hard surfaces
A comeback Medvedev secured his maiden trophy for 882 days with success over Frenchman Moutet in the competition final.
The athlete, a ex- top-ranked player, has had a challenging period, winning just one match at the big events and undergoing a meltdown at the American major.
Medvedev's unpredictability on the professional circuit - and difficulties with his serving in particular - caused him falling of the world's top 10 and eventually parting ways with former coach his previous coach.
Presently training with Thomas Johansson and Rohan Goetzke, the tennis star has steadily advanced in the last few weeks - culminating in a hard-fought competitive triumph over Frenchman Moutet.
This marks Medvedev's initial championship since the 2023 Rome Masters and first on a hard surface from that period of 2023.
Victory also means he has achieved twenty-one titles at 21 distinct competitions.
"It's the first time I'm at a competition with my two daughters together, so to secure a championship is particularly special," commented ranked player Medvedev.
"This championship is in tribute of my second daughter my daughter, because the first title I achieved when my first daughter my daughter was delivered was for her."
The tennis star, the 2021 US Open champion, had lost his previous six championship matches, featuring in the German tournament earlier this year.
The player's retrieving strategy and regular emotional displays on the tennis court had prompted observers to doubt if his capacity to perform at the top level was concluded.
Yet the athlete has made changes in recent weeks, attempting to advance forward and perform aggressively, backed up by an improved serve.
The champion fought back from a disadvantage in the opening set against the tricky Moutet, taking four of the concluding five points to take the lead.
Both players exchanged break points in the second set before the challenger, bidding for his initial tour championship, gained dominance to push for a third set.
He saved four early-game break points in a competitive final set before Medvedev secured a break to fifteen to serve for the match.
Fittingly, he secured the win with a shot at the net, with Moutet unable to manage a return after a lengthy match.
