Nineteen of Medvedev's twenty-one titles have been achieved on hard courts
A resurgent Medvedev claimed his initial championship for 882 days with success over opponent Moutet in the competition title decider.
The athlete, a ex- world number one, has had a challenging period, achieving just a single victory at the big events and undergoing a difficult moment at the US Open.
Medvedev's inconsistency on the professional circuit - and struggles with his service game in specific - led to him falling of the top ten and eventually separating with former trainer Gilles Cervara.
Presently working with Thomas Johansson and Goetzke, he has gradually improved in the past month - climaxing in a hard-fought three-set win over challenger Corentin Moutet.
This represents the player's maiden championship after the Italian tournament and initial on a hard court from spring of 2023.
Victory also means he has won 21 victories at twenty-one different events.
"This marks the first occasion I have attended a tournament with my children simultaneously, so to secure a title is really nice," commented world number 14 Medvedev.
"This victory is in tribute of my child my daughter, because the initial championship I got when my child Alisa was born was for her."
The athlete, the 2021 US Open champion, had failed in his previous six finals, comprising in that event previously this season.
The player's retrieving play style and regular emotional displays on the tennis court had led observers to question if his skill to compete at the elite level was concluded.
But the player has altered his approach in recent weeks, striving to advance forward and perform aggressively, supported by an enhanced serve.
Medvedev fought back from a deficit in the opening set against the challenging Moutet, winning four of the final five points to go ahead.
The pair exchanged break points in the middle set before Moutet, bidding for his first ATP Tour title, gained dominance to push for a final set.
Moutet rescued four early break points in a tight final set before Medvedev won the break to fifteen to secure the win.
Appropriately, he clinched the win with a point at the net, with his opponent incapable to manage a volley after two hours and 38 minutes.