Nineteen of Medvedev's twenty-one championships have been achieved on hard courts
A resurgent Medvedev secured his maiden trophy for 882 days with a win over Frenchman Moutet in the competition title decider.
Medvedev, a ex- top-ranked player, has had a challenging year, achieving just one match at the major tournaments and suffering a difficult moment at the US Open.
The player's inconsistency on the ATP Tour - and struggles with his serve in specific - led to him exiting of the top ten and eventually parting ways with long-term mentor Cervara.
Now working with Johansson and Goetzke, he has gradually advanced in the last few weeks - peaking in a tightly fought three-set win over opponent Moutet.
It is the player's maiden title following the Italian tournament and first on a hardcourt since spring of that year.
Victory also means Medvedev has won 21 victories at 21 various events.
"It's the first time I am participating in a competition with my children together, so to win a championship is really nice," said world number 14 the champion.
"This championship is in dedication of my second daughter her name, because the first title I achieved when my older daughter my daughter was born was for her."
Medvedev, the 2021 US Open champion, had failed in his past six title deciders, comprising in that event earlier this year.
His defensive strategy and frequent emotional displays on court had caused some to wonder if his skill to perform at the top level was over.
However the 29-year-old has made changes in the past month, striving to advance forward and compete positively, backed up by an better serving game.
The champion fought back from a deficit in the first set against the difficult Frenchman, securing four of the last five games to go ahead.
The pair exchanged service breaks in the second set before the Frenchman, striving for his maiden ATP Tour championship, seized the initiative to create a final set.
He defended four early chances in a competitive deciding set before the champion won the break to that score to secure the win.
Suitably, the winner secured victory with a point at the net, with the Frenchman unable to manage a shot after a lengthy match.