19 of the Russian's 21 titles have been won on hard courts
A resurgent the Russian player claimed his maiden trophy for over two years with success over Frenchman Moutet in the tournament final.
Medvedev, a ex- top-ranked player, has experienced a torrid period, managing just one match at the big events and undergoing a setback at the New York tournament.
The player's unpredictability on the ATP Tour - and struggles with his serve in especial - caused him falling of the elite rankings and eventually parting ways with long-term mentor Gilles Cervara.
Currently working with Johansson and Rohan Goetzke, he has consistently advanced in the last few weeks - culminating in a closely contested three-set triumph over Frenchman Moutet.
This represents Medvedev's initial title since the Italian tournament and maiden on a hard court after March of that year.
The win also signifies Medvedev has won twenty-one championships at twenty-one various tournaments.
"It's the first time I am participating in a event with my both daughters at once, so to win a trophy is especially meaningful," commented world number 14 the champion.
"This victory is in honour of my younger daughter my daughter, because the first title I achieved when my older daughter my daughter was delivered was for her."
Medvedev, the past champion, had lost his last six finals, including in Halle in the past months.
Medvedev's retrieving approach and recurring emotional displays on the playing surface had led commentators to doubt if his capacity to perform at the top level was over.
However the 29-year-old has made changes in recent weeks, striving to come to the net and play positively, supported by an improved service.
Medvedev fought back from a deficit in the first set against the difficult Frenchman, winning four of the final five exchanges to take the lead.
The competitors exchanged service breaks in the middle set before Moutet, striving for his maiden ATP Tour victory, gained dominance to push for a final set.
The opponent defended four early opportunities in a close final set before Medvedev secured a break to that score to secure the win.
Appropriately, Medvedev earned the title with a shot at the front of the court, with Moutet unable to control a volley after two hours and 38 minutes.
