Nineteen of the Russian's twenty-one championships have been won on hard surfaces
A comeback Medvedev secured his initial trophy for nearly 30 months with victory over Frenchman Moutet in the competition final.
The Russian, a former number one, has had a difficult period, winning just one match at the big events and undergoing a setback at the New York tournament.
The player's varied form on the professional circuit - and difficulties with his service game in especial - caused him falling of the elite rankings and eventually parting ways with long-time trainer his previous coach.
Currently working with his coach and Goetzke, the tennis star has consistently improved in the last few weeks - peaking in a hard-fought competitive triumph over challenger Corentin Moutet.
This marks Medvedev's first trophy following the Rome competition and maiden on a hard surface from spring of the previous year.
Success also signifies Medvedev has achieved 21 titles at 21 different tournaments.
"This marks the first occasion I'm at a tournament with my two daughters at once, so to get a championship is especially meaningful," stated world number 14 Medvedev.
"This championship is in honour of my younger daughter her name, because the maiden victory I achieved when my older daughter Alisa was born was for her."
The tennis star, the former major winner, had lost his last six championship matches, comprising in that event earlier this year.
Medvedev's counter-punching approach and regular outbursts on the tennis court had led observers to question if his ability to compete at the top level was over.
However the player has made changes in the past month, attempting to come to the net and compete assertively, supported by an improved service.
He came back from a disadvantage in the opening set against the difficult Frenchman, securing 4 of the concluding five exchanges to take the lead.
The competitors swapped service breaks in the middle set before the challenger, bidding for his maiden professional victory, took control to push for a final set.
Moutet rescued four early-game opportunities in a close third set before Medvedev broke to that score to secure the win.
Appropriately, he earned the win with a point at the net area, with Moutet unable to handle a volley after a lengthy match.
