Nineteen of the Russian's twenty-one titles have been won on hard courts
A comeback Medvedev claimed his first trophy for 882 days with victory over opponent Moutet in the tournament title decider.
Medvedev, a ex- world number one, has experienced a difficult year, winning just one win at the Grand Slams and experiencing a setback at the American major.
The player's unpredictability on the professional circuit - and issues with his serving in particular - resulted in him dropping out of the world's top 10 and ultimately parting ways with long-time trainer Cervara.
Now working with Thomas Johansson and Rohan Goetzke, Medvedev has steadily advanced in the last few weeks - culminating in a hard-fought 7-5 4-6 6-3 victory over Frenchman Moutet.
This marks Medvedev's maiden title after the 2023 Rome Masters and first on a hardcourt from March of that year.
Success also indicates Medvedev has achieved 21 victories at twenty-one distinct competitions.
"For the first time I am participating in a event with my two daughters together, so to get a championship is really nice," said tennis professional the champion.
"This title is in honour of my child her name, because the initial championship I got when my first daughter my daughter was born was for her."
Medvedev, the former major winner, had failed in his last six title deciders, featuring in Halle previously this season.
Medvedev's retrieving strategy and regular emotional displays on court had caused observers to wonder if his ability to perform at the top level was finished.
However the player has altered his approach in recent weeks, attempting to come to the net and play assertively, backed up by an improved serving game.
The champion came back from a deficit in the opening set against the tricky Frenchman, securing four of the final five points to gain the advantage.
The pair traded service breaks in the following set before the Frenchman, attempting for his initial tour victory, seized the initiative to push for a decider.
He saved four early-game break points in a close final set before the champion broke to fifteen to secure the win.
Appropriately, Medvedev secured the title with a rally at the net, with Moutet unable to control a volley after a lengthy match.
