Nineteen of the Russian's 21 championships have been achieved on hard surfaces
A comeback Medvedev won his initial title for 882 days with victory over Frenchman Moutet in the tournament title decider.
The athlete, a ex- world number one, has had a challenging period, achieving just one match at the big events and suffering a difficult moment at the New York tournament.
The player's unpredictability on the professional circuit - and struggles with his serving in especial - caused him dropping out of the top ten and finally separating with long-term mentor his previous coach.
Currently collaborating with Thomas Johansson and his other coach, he has steadily advanced in the last few weeks - climaxing in a closely contested 7-5 4-6 6-3 victory over Frenchman Moutet.
This represents the player's maiden title following the Rome competition and initial on a hard surface after March of 2023.
Victory also means Medvedev has secured 21 titles at twenty-one distinct competitions.
"It's the first time I'm at a event with my both daughters at once, so to secure a title is especially meaningful," said ranked player the champion.
"This championship is in dedication of my child her name, because the initial championship I got when my older daughter Alisa was delivered was for her."
The athlete, the 2021 US Open champion, had been defeated in his previous six finals, including in the German tournament earlier this year.
The player's counter-punching strategy and recurring outbursts on the tennis court had led some to doubt if his ability to perform at the top level was over.
Yet the athlete has made changes in recent weeks, attempting to come to the net and perform positively, supported by an better service.
Medvedev fought back from a deficit in the initial set against the challenging Moutet, taking 4 of the last five games to gain the advantage.
Both players exchanged breaks in the following set before Moutet, striving for his maiden tour championship, gained dominance to push for a third set.
Moutet defended 4 early chances in a competitive deciding set before the champion secured a break to that score to close out the victory.
Fittingly, Medvedev earned victory with a point at the net area, with the Frenchman unable to control a shot after a lengthy match.
