Nineteen of the Russian's 21 victories have been achieved on hard courts
A comeback Medvedev won his initial championship for over two years with victory over Frenchman Moutet in the Almaty Open championship match.
The Russian, a ex- top-ranked player, has experienced a difficult period, managing just a single victory at the big events and suffering a meltdown at the US Open.
His varied form on the ATP Tour - and difficulties with his service game in specific - caused him dropping out of the world's top 10 and eventually separating with former mentor his previous coach.
Now collaborating with Johansson and Rohan Goetzke, he has steadily progressed in the past month - climaxing in a hard-fought three-set win over opponent Corentin Moutet.
This marks Medvedev's first title after the Italian tournament and first on a hard surface from spring of 2023.
The win also signifies Medvedev has won twenty-one championships at twenty-one different events.
"It's the first time I'm at a tournament with my both daughters simultaneously, so to get a championship is especially meaningful," commented world number 14 Medvedev.
"This title is in honour of my younger daughter her name, because the maiden victory I achieved when my child Alisa was born was for her."
Medvedev, the former major winner, had been defeated in his previous six title deciders, comprising in the German tournament previously this season.
The player's counter-punching approach and recurring emotional displays on the tennis court had prompted commentators to question if his skill to compete at the highest level was concluded.
But the 29-year-old has altered his approach in recent weeks, striving to approach the net and perform aggressively, reinforced by an improved service.
Medvedev recovered from a disadvantage in the opening set against the difficult opponent, securing four of the last five exchanges to gain the advantage.
Both players swapped break points in the second set before the Frenchman, attempting for his maiden professional title, seized the initiative to create a final set.
He rescued 4 early-game break points in a close deciding set before Medvedev secured a break to that score to secure the win.
Suitably, the winner secured the title with a rally at the net, with Moutet unable to handle a shot after two hours and 38 minutes.
