19 of Medvedev's 21 championships have been won on hard surfaces
A resurgent Medvedev won his maiden championship for 882 days with a win over opponent Moutet in the tournament final.
The Russian, a former world number one, has experienced a torrid season, achieving just one match at the Grand Slams and suffering a difficult moment at the US Open.
His varied form on the professional circuit - and issues with his serving in specific - caused him exiting of the elite rankings and ultimately splitting with long-term coach Cervara.
Now training with Johansson and his other coach, he has steadily improved in the last few weeks - culminating in a closely contested competitive win over challenger Moutet.
This marks Medvedev's initial title after the 2023 Rome Masters and initial on a hard court from March of the previous year.
Victory also indicates the Russian has achieved twenty-one titles at 21 various events.
"It's the first time I am participating in a competition with my children at once, so to get a trophy is especially meaningful," said world number 14 Medvedev.
"This championship is in dedication of my second daughter my daughter, because the first title I achieved when my child her name was delivered was for her."
Medvedev, the former major winner, had lost his previous six finals, comprising in Halle previously this season.
His retrieving strategy and frequent reactions on the playing surface had led some to doubt if his skill to play at the elite level was finished.
Yet the 29-year-old has altered his approach in the last few weeks, attempting to advance forward and play assertively, reinforced by an improved serve.
He recovered from a break down in the initial set against the difficult opponent, securing four of the concluding five points to gain the advantage.
The competitors swapped break points in the second set before Moutet, bidding for his first ATP Tour championship, took control to create a decider.
The opponent saved four early-game break points in a competitive deciding set before the Russian broke to that score to secure the win.
Fittingly, the winner clinched the win with a shot at the net area, with his opponent incapable to control a shot after a lengthy match.
