Nineteen of the Russian's twenty-one victories have been won on hard courts
A comeback Medvedev claimed his maiden title for 882 days with success over opponent Moutet in the Almaty Open championship match.
The Russian, a ex- number one, has endured a difficult period, achieving just one match at the major tournaments and experiencing a setback at the American major.
His inconsistency on the professional circuit - and issues with his serve in specific - caused him exiting of the elite rankings and ultimately separating with long-term coach Cervara.
Currently working with Johansson and Rohan Goetzke, Medvedev has consistently improved in the recent weeks - peaking in a closely contested 7-5 4-6 6-3 triumph over Frenchman Moutet.
It is his maiden trophy after the Italian tournament and first on a hardcourt from spring of the previous year.
Victory also signifies he has won twenty-one titles at 21 different events.
"For the first time I have attended a competition with my children together, so to get a title is particularly special," commented world number 14 Daniil Medvedev.
"This title is in dedication of my child Victoria, because the first title I achieved when my first daughter her name was born was for her."
Medvedev, the former major winner, had been defeated in his previous six title deciders, featuring in Halle in the past months.
Medvedev's counter-punching strategy and recurring outbursts on court had caused observers to question if his ability to perform at the top level was concluded.
But the 29-year-old has altered his approach in recent weeks, attempting to come to the net and perform positively, reinforced by an improved serve.
The champion came back from a break down in the opening set against the tricky Moutet, winning four of the final five points to gain the advantage.
Both players swapped break points in the second set before Moutet, attempting for his initial professional title, gained dominance to push for a third set.
The opponent saved four early-game chances in a close third set before the champion won the break to that score to close out the victory.
Appropriately, Medvedev earned the title with a point at the net, with the Frenchman unable to handle a return after two hours and 38 minutes.
