19 of Medvedev's twenty-one titles have been earned on hard surfaces
A comeback Medvedev won his first trophy for nearly 30 months with success over opponent Moutet in the competition title decider.
The Russian, a former top-ranked player, has endured a difficult period, achieving just a single victory at the major tournaments and experiencing a meltdown at the American major.
The player's unpredictability on the tennis tour - and issues with his serve in especial - led to him falling of the top ten and eventually separating with long-term coach Gilles Cervara.
Presently working with his coach and his other coach, he has consistently improved in the past month - peaking in a closely contested three-set triumph over challenger Moutet.
This marks Medvedev's initial championship after the Rome competition and maiden on a hardcourt after that period of the previous year.
The win also indicates the Russian has achieved 21 victories at twenty-one distinct events.
"This marks the first occasion I'm at a competition with my children together, so to secure a title is particularly special," said world number 14 Medvedev.
"This title is in honour of my child my daughter, because the initial championship I won when my child Alisa was born was for her."
The athlete, the past champion, had lost his last six finals, featuring in the German tournament in the past months.
The player's defensive strategy and frequent emotional displays on the playing surface had prompted commentators to wonder if his skill to compete at the top level was over.
However the athlete has made changes in recent weeks, making an effort to approach the net and compete aggressively, reinforced by an improved serving game.
He came back from a deficit in the opening set against the challenging Moutet, winning 4 of the concluding five points to gain the advantage.
The pair swapped break points in the middle set before the challenger, attempting for his maiden ATP Tour victory, took control to force a final set.
The opponent saved four early-game break points in a close third set before the champion broke to fifteen to close out the victory.
Suitably, he earned the title with a shot at the net area, with Moutet incapable to manage a shot after a lengthy match.