Nineteen of the Russian's 21 titles have been earned on hard surfaces
A comeback Medvedev claimed his initial trophy for nearly 30 months with a win over opponent Moutet in the competition championship match.
Medvedev, a ex- top-ranked player, has had a difficult period, winning just one match at the big events and suffering a setback at the US Open.
His unpredictability on the tennis tour - and issues with his serving in particular - caused him dropping out of the world's top 10 and finally splitting with former trainer Cervara.
Now collaborating with Johansson and Rohan Goetzke, Medvedev has gradually progressed in the past month - peaking in a closely contested competitive triumph over opponent Corentin Moutet.
It is the player's initial championship following the Rome competition and maiden on a hard surface since March of the previous year.
The win also indicates the Russian has achieved twenty-one victories at twenty-one various events.
"It's the first time I'm at a tournament with my children together, so to secure a trophy is particularly special," commented tennis professional the champion.
"This championship is in honour of my child my daughter, because the maiden victory I got when my first daughter Alisa was born was for her."
Medvedev, the past champion, had failed in his previous six championship matches, featuring in that event earlier this year.
His counter-punching play style and regular reactions on the tennis court had caused some to wonder if his capacity to play at the top level was finished.
However the athlete has made changes in the last few weeks, attempting to approach the net and play aggressively, supported by an improved service.
Medvedev fought back from a break down in the opening set against the tricky opponent, winning 4 of the last five exchanges to gain the advantage.
The pair swapped service breaks in the middle set before Moutet, bidding for his initial professional victory, gained dominance to create a decider.
Moutet defended four early chances in a competitive third set before the Russian secured a break to that score to serve for the match.
Fittingly, the winner earned victory with a rally at the net area, with the Frenchman incapable to control a volley after two hours and 38 minutes.
