It is the latest breakthrough moment in a season of them for the 23-year-old Yorkshireman, who reached his first grand slam semi-final at the Australian Open in January, became British number one and climbed into the world's top 20.
Edmund struggled with the occasion in his first ATP final in Marrakech earlier this season but held his nerve superbly here, coming from a set down to see off his highly-experienced opponent 3-6 7-6 (2) 7-6 (4).
Edmund had made no secret of his desire to win a title sooner rather than later and he was in tears as he embraced his support team.
One break of serve proved enough for Monfils to take the opening set and the flamboyant Frenchman recovered from a break down to take the second to a tie-break, which top seed Edmund dominated.
It took another tie-break to decide the match after both men saved two break points in the third set, and this one was much tighter, but a mini-break for 5-3 proved crucial for Edmund, who clinched victory on his first match point.
Edmund will climb back to 14th in the world rankings, equalling his career high, but his hopes of qualifying for the ATP Finals in London for the first time remain extremely remote, with this tournament offering only 250 points for the winner.
It continued his fine form since a first-round loss at the US Open, though, following on from a semi-final appearance in Beijing and quarter-final at the Shanghai Masters.
Another man who has had an excellent 2018, 20-year-old Greek Stefanos Tsitsipas, also won his first ATP Tour title, defeating Ernests Gulbis 6-4 6-4 at the Stockholm Open.
There was a home winner at the Kremlin Cup as Russian Karen Khachanov defeated France's Adrian Mannarino 6-2 6-2 in less than an hour to claim his third ATP Tour crown.
Edmund was not the only British winner, meanwhile, with Luke Bambridge and Jonny O'Mara defeating third seeds Marcus Daniell of New Zealand and Dutchman Wesley Koolhof 7-5 7-6 (8) to take the doubles title in Stockholm.