19 of the Russian's 21 titles have been won on hard courts
A comeback Medvedev claimed his initial championship for nearly 30 months with success over Frenchman Moutet in the Almaty Open championship match.
The Russian, a ex- world number one, has endured a difficult year, winning just a single victory at the big events and suffering a setback at the US Open.
The player's unpredictability on the tennis tour - and struggles with his serve in particular - caused him exiting of the elite rankings and eventually parting ways with long-term mentor Gilles Cervara.
Currently training with Johansson and his other coach, Medvedev has consistently progressed in the recent weeks - culminating in a tightly fought 7-5 4-6 6-3 triumph over challenger Corentin Moutet.
This represents Medvedev's maiden championship after the Italian tournament and maiden on a hard court from spring of that year.
Success also means Medvedev has achieved 21 victories at twenty-one various events.
"This marks the first occasion I am participating in a tournament with my two daughters at once, so to win a trophy is especially meaningful," stated ranked player Medvedev.
"This championship is in honour of my younger daughter her name, because the initial championship I got when my first daughter her name was born was for her."
The tennis star, the past champion, had been defeated in his past six title deciders, featuring in Halle previously this season.
His counter-punching strategy and regular emotional displays on court had led some to doubt if his ability to perform at the elite level was concluded.
But the athlete has altered his approach in the past month, attempting to approach the net and perform positively, supported by an improved service.
Medvedev recovered from a break down in the initial set against the challenging Frenchman, winning 4 of the last five games to go ahead.
Both players exchanged breaks in the following set before the Frenchman, striving for his initial tour victory, took control to create a final set.
The opponent rescued 4 early-game break points in a close final set before Medvedev won the break to that score to serve for the match.
Suitably, he earned the title with a shot at the net area, with the Frenchman failing to handle a shot after two hours and 38 minutes.