Nineteen of Medvedev's 21 titles have been won on hard surfaces
A comeback the Russian player secured his first championship for 882 days with a win over opponent Moutet in the competition title decider.
The athlete, a former top-ranked player, has endured a challenging year, managing just one match at the major tournaments and experiencing a meltdown at the US Open.
His inconsistency on the ATP Tour - and issues with his serving in specific - resulted in him exiting of the world's top 10 and ultimately separating with long-term mentor his previous coach.
Now training with Johansson and his other coach, he has steadily progressed in the past month - peaking in a hard-fought 7-5 4-6 6-3 triumph over opponent Corentin Moutet.
It is the player's first title following the Italian tournament and maiden on a hard court from spring of the previous year.
Victory also indicates Medvedev has achieved 21 titles at twenty-one different tournaments.
"This marks the first occasion I have attended a event with my two daughters simultaneously, so to win a championship is particularly special," commented world number 14 the champion.
"This championship is in honour of my child Victoria, because the first title I won when my child my daughter was delivered was for her."
The tennis star, the former major winner, had been defeated in his past six championship matches, including in that event earlier this year.
Medvedev's defensive approach and recurring outbursts on the playing surface had caused observers to doubt if his skill to play at the top level was finished.
However the player has implemented adjustments in the past month, making an effort to come to the net and perform aggressively, supported by an enhanced serving game.
Medvedev fought back from a disadvantage in the initial set against the tricky Moutet, securing four of the last five points to take the lead.
The competitors traded service breaks in the second set before the challenger, bidding for his initial professional title, took control to force a decider.
The opponent rescued four early-game chances in a close deciding set before the Russian won the break to 15 to serve for the match.
Suitably, the winner clinched the title with a rally at the net area, with the Frenchman unable to control a return after two hours and 38 minutes.
