19 of the Russian's 21 championships have been earned on hardcourt
A comeback Medvedev won his maiden championship for 882 days with a win over opponent Moutet in the competition final.
Medvedev, a former number one, has experienced a torrid period, achieving just one match at the Grand Slams and suffering a meltdown at the American major.
His varied form on the tennis tour - and struggles with his serve in specific - led to him falling of the elite rankings and eventually separating with long-time trainer Cervara.
Now working with Thomas Johansson and Goetzke, he has consistently advanced in the past month - culminating in a closely contested three-set win over Frenchman Moutet.
This represents Medvedev's first championship after the Italian tournament and maiden on a hard surface since spring of that year.
The win also indicates he has won twenty-one titles at 21 distinct events.
"For the first time I have attended a tournament with my both daughters at once, so to get a championship is really nice," said world number 14 the champion.
"This title is in dedication of my child Victoria, because the initial championship I got when my older daughter my daughter was delivered was for her."
Medvedev, the past champion, had lost his last six title deciders, comprising in that event earlier this year.
His counter-punching play style and recurring reactions on court had led commentators to question if his capacity to play at the elite level was over.
However the 29-year-old has implemented adjustments in recent weeks, attempting to approach the net and play aggressively, supported by an improved serve.
The champion fought back from a break down in the first set against the tricky Moutet, securing four of the concluding five points to take the lead.
The pair traded break points in the second set before Moutet, bidding for his initial tour title, took control to create a final set.
Moutet defended 4 early-game chances in a close third set before the champion won the break to that score to secure the win.
Fittingly, Medvedev earned victory with a shot at the net area, with Moutet unable to manage a volley after two hours and 38 minutes.
