19 of Medvedev's 21 victories have been earned on hard surfaces
A resurgent the Russian player secured his initial title for 882 days with success over opponent Moutet in the tournament championship match.
The athlete, a former world number one, has experienced a challenging period, achieving just one match at the Grand Slams and suffering a meltdown at the US Open.
His inconsistency on the ATP Tour - and struggles with his service game in specific - resulted in him falling of the world's top 10 and ultimately parting ways with former mentor Cervara.
Presently working with Thomas Johansson and his other coach, Medvedev has steadily progressed in the last few weeks - climaxing in a hard-fought competitive win over Frenchman Moutet.
This marks his initial championship since the Italian tournament and initial on a hard surface since spring of 2023.
Success also signifies Medvedev has achieved 21 titles at 21 various tournaments.
"For the first time I'm at a competition with my both daughters simultaneously, so to get a title is particularly special," stated world number 14 the champion.
"This title is in honour of my younger daughter her name, because the maiden victory I got when my older daughter my daughter was born was for her."
Medvedev, the past champion, had failed in his last six title deciders, featuring in Halle previously this season.
The player's counter-punching play style and regular reactions on the tennis court had caused observers to doubt if his capacity to play at the highest level was concluded.
But the 29-year-old has altered his approach in the past month, striving to advance forward and perform aggressively, reinforced by an improved serve.
The champion fought back from a deficit in the first set against the difficult opponent, securing 4 of the concluding five points to take the lead.
The pair swapped service breaks in the following set before the challenger, striving for his initial tour title, gained dominance to push for a decider.
The opponent saved four initial break points in a tight deciding set before the Russian broke to that score to close out the victory.
Appropriately, Medvedev clinched the win with a shot at the net area, with Moutet incapable to control a volley after over two and a half hours.