Monfils, the runner-up three years ago, held off Wawrinka's second-set surge to ease through the decider.
"It was an unbelievable week, a pleasure," said Monfils.
"Stan is a part of this win. We've been talking a lot and practising a lot. You're my brother," he told his Swiss opponent.
"This has been a good week for Stan and a good week for me. I hope we can have many more battles."
Wawrinka, the 2015 champion in the Dutch port city who is continuing an 18-month comeback from double knee surgery, was playing in his first final since Roland Garros in June 2017.
"It was great for sure to be in the final," Wawrinka said. "I'm pleased with the way I played in it and the way I arrived to the final.
"I played four good matches here, I kept my level up all week."
Three-time major winner Wawrinka said he hopes to build on his run this week.
"I need to keep doing what I've been doing the last few months. I need to play events to gain confidence. Keeping going is the only way to get back my ranking," said the world number 68.
It was the first championship match in 11 years at Rotterdam to feature two unseeded players.
Monfils, 32, showed no hard evidence of the left wrist injury which has bothered him all week and forced him onto a regime of pain-killers.
"I struggled with the wrist all week," he said. "I came out running hard in the first game to make him feel I was there.
"But when I hit as hard as I could with the backhand -- 'ohhh'," he said in reference to the wrist pain he was feeling.
"I've been in worse shape, but I'm really exhausted after this week."
The world number 33 triumphed in one and three-quarter hours with four service breaks against three-time major winner Wawrinka as he claimed his first title since Doha last year.
The Frenchman took the opening set with two breaks of Wawrinka, but the 33-year-old Swiss immediately returned the favour with a 6-1 second set.
In the third, Monfils broke for 2-1, taking control of his opponent's mighty backhand.
The Frenchman moved to 5-2 and saved a break point a game later as he closed out victory.