Nineteen of Medvedev's 21 titles have been achieved on hard surfaces
A comeback the Russian player won his first title for over two years with victory over opponent Moutet in the competition title decider.
Medvedev, a ex- world number one, has endured a difficult season, managing just a single victory at the big events and experiencing a meltdown at the New York tournament.
His unpredictability on the professional circuit - and difficulties with his serving in especial - resulted in him falling of the world's top 10 and eventually separating with long-time trainer Gilles Cervara.
Presently training with his coach and Goetzke, the tennis star has steadily improved in the last few weeks - climaxing in a tightly fought three-set win over challenger Corentin Moutet.
This represents his first trophy following the 2023 Rome Masters and first on a hard court from March of the previous year.
The win also indicates the Russian has secured 21 victories at 21 distinct events.
"It's the first time I am participating in a competition with my two daughters together, so to win a championship is particularly special," stated ranked player Daniil Medvedev.
"This championship is in honour of my child my daughter, because the first title I got when my older daughter Alisa was born was for her."
The athlete, the past champion, had failed in his last six championship matches, featuring in Halle earlier this year.
His counter-punching play style and recurring emotional displays on the playing surface had led observers to question if his skill to perform at the elite level was finished.
But the player has made changes in the last few weeks, striving to approach the net and play assertively, reinforced by an enhanced service.
Medvedev fought back from a break down in the opening set against the tricky opponent, securing four of the last five games to take the lead.
The competitors swapped service breaks in the second set before Moutet, bidding for his initial tour title, took control to force a third set.
Moutet defended four early break points in a tight deciding set before the champion won the break to fifteen to serve for the match.
Suitably, he secured victory with a shot at the net, with the Frenchman incapable to manage a volley after a lengthy match.