Nineteen of Medvedev's 21 titles have been achieved on hard surfaces
A resurgent Medvedev secured his first trophy for 882 days with success over opponent Moutet in the Almaty Open title decider.
Medvedev, a ex- top-ranked player, has had a difficult season, managing just one win at the Grand Slams and suffering a meltdown at the US Open.
Medvedev's varied form on the tennis tour - and difficulties with his service game in particular - resulted in him dropping out of the world's top 10 and ultimately parting ways with former mentor his previous coach.
Now collaborating with Johansson and Rohan Goetzke, Medvedev has consistently progressed in the last few weeks - climaxing in a tightly fought three-set triumph over opponent Moutet.
This marks Medvedev's first championship following the Italian tournament and first on a hard court after that period of the previous year.
The win also indicates he has achieved 21 titles at twenty-one various tournaments.
"It's the first time I am participating in a event with my both daughters together, so to get a trophy is particularly special," commented tennis professional the champion.
"This championship is in tribute of my child my daughter, because the first title I got when my child my daughter was born was for her."
Medvedev, the past champion, had lost his past six championship matches, comprising in Halle in the past months.
His defensive strategy and frequent emotional displays on the tennis court had caused commentators to wonder if his skill to compete at the top level was concluded.
But the athlete has made changes in the past month, striving to come to the net and compete positively, reinforced by an improved serve.
He came back from a disadvantage in the opening set against the challenging Frenchman, securing 4 of the concluding five exchanges to gain the advantage.
Both players exchanged breaks in the second set before the challenger, bidding for his initial professional victory, gained dominance to create a final set.
Moutet defended four early-game opportunities in a tight final set before the champion won the break to that score to close out the victory.
Fittingly, the winner secured victory with a point at the net area, with his opponent incapable to control a shot after a lengthy match.