Nineteen of the Russian's twenty-one titles have been earned on hard surfaces
A resurgent the Russian player claimed his initial title for nearly 30 months with a win over opponent Moutet in the competition final.
The athlete, a ex- number one, has experienced a challenging season, managing just one match at the major tournaments and suffering a difficult moment at the US Open.
The player's unpredictability on the professional circuit - and difficulties with his service game in particular - resulted in him exiting of the world's top 10 and finally separating with long-term coach Cervara.
Presently working with Thomas Johansson and his other coach, Medvedev has steadily progressed in the past month - peaking in a tightly fought 7-5 4-6 6-3 triumph over challenger Moutet.
It is his first championship after the Rome competition and maiden on a hard court since that period of the previous year.
The win also signifies Medvedev has achieved 21 titles at twenty-one distinct events.
"This marks the first occasion I'm at a tournament with my both daughters simultaneously, so to secure a trophy is particularly special," commented ranked player Medvedev.
"This championship is in honour of my younger daughter her name, because the maiden victory I got when my older daughter Alisa was born was for her."
The tennis star, the past champion, had been defeated in his past six title deciders, including in Halle earlier this year.
His defensive play style and frequent reactions on court had caused commentators to question if his ability to play at the elite level was concluded.
Yet the player has made changes in the last few weeks, making an effort to approach the net and play positively, backed up by an improved serving game.
Medvedev recovered from a disadvantage in the opening set against the tricky Moutet, winning four of the last five points to go ahead.
The competitors swapped service breaks in the middle set before Moutet, attempting for his maiden tour title, took control to create a third set.
The opponent saved four initial chances in a close deciding set before Medvedev secured a break to 15 to close out the victory.
Suitably, Medvedev secured the title with a rally at the net area, with Moutet failing to handle a shot after two hours and 38 minutes.