Nineteen of Medvedev's 21 titles have been earned on hard surfaces
A comeback the Russian player secured his first championship for over two years with a win over opponent Moutet in the tournament final.
Medvedev, a ex- number one, has had a challenging period, managing just one win at the Grand Slams and suffering a meltdown at the US Open.
The player's unpredictability on the tennis tour - and difficulties with his serve in particular - led to him dropping out of the top ten and ultimately separating with long-time mentor Cervara.
Presently collaborating with Thomas Johansson and his other coach, Medvedev has steadily improved in the last few weeks - climaxing in a closely contested 7-5 4-6 6-3 win over opponent Moutet.
This marks the player's maiden trophy following the Italian tournament and maiden on a hard surface from spring of 2023.
The win also indicates the Russian has achieved 21 titles at twenty-one distinct tournaments.
"It's the first time I'm at a tournament with my children simultaneously, so to win a championship is especially meaningful," stated ranked player the champion.
"This victory is in honour of my child my daughter, because the initial championship I achieved when my first daughter Alisa was born was for her."
The tennis star, the 2021 US Open champion, had lost his previous six finals, featuring in Halle earlier this year.
His retrieving approach and regular emotional displays on the playing surface had caused observers to question if his skill to compete at the top level was concluded.
However the player has implemented adjustments in the past month, striving to come to the net and perform positively, supported by an enhanced service.
Medvedev fought back from a disadvantage in the first set against the difficult Frenchman, winning 4 of the final five points to take the lead.
The pair swapped service breaks in the following set before Moutet, striving for his first tour title, seized the initiative to push for a decider.
Moutet rescued 4 early-game chances in a competitive deciding set before Medvedev secured a break to fifteen to secure the win.
Fittingly, Medvedev clinched victory with a shot at the front of the court, with his opponent failing to manage a volley after a lengthy match.