Both artists, whose post-impressionist paintings are known worldwide, signed the letter that is dated November 1/2, 1888, less than two years before Van Gogh died at the age of 37. It was addressed to their painter friend Emile Bernard.
The correspondence was penned in the French city of Arles, where the Dutch painter had been staying since February of that year.
This was not long after Van Gogh produced some of his most famous work including Bedroom in Arles, Van Gogh's Chair and some of his Sunflowers series.
At the time of writing, he had recently been joined by Gauguin, who he had first met in Paris two years earlier.
Gauguin arrived in Arles, where Van Gogh was living, on October 23, 1888 and the two spent several stormy months painting together.
It was during the fateful visit that Van Gogh lost his ear, presenting it to a brothel maid.
The incident effectively ended his often strained relationship with Gauguin.
The letter is "exceptional" because the artists described their certainty that their paintings would revolutionize art in the future, stated Drouot auction house, where the letter was sold.
"This document reflects the immense lucidity of these artists in terms of the change taking place around them: they are fully aware that their art marks a turning point and that only future generations will understand it," Drouot adds in the statement.
Une lettre de la main de deux immenses peintres, Vincent #VanGogh & Paul #Gauguin, adressée à Emile Bernard bientôt aux enchères !— Drouot (@Drouot) June 12, 2020
Le texte des deux artistes exprime leur certitude que leur peinture va révolutionner l'art des générations futures.
Et comme ils avaient raison. pic.twitter.com/Tn286WrRKH
The Dutchman also writes about his visitor and their escapades.
"Gauguin interests me a lot as a man," he said.
"It has long seemed to me that in our dirty profession of painter, we have the greatest need for people with workers' hands and stomachs, with more natural tastes, more loving and more charitable temperaments than the decadent and exhausted Parisian boulevardier."
He describes Gauguin as "a virgin being with wild animal instincts. In Gauguin, blood and sex prevail over ambition.
"We made some excursions to the brothels and it is probable that we will often end up going to work there."
Van Gogh yields the pen on the last page to Gauguin who would have a successful sale of paintings at Drouot in 1891.
"Do not listen to Vincent," he wrote. "As you know he is easy to impress."
As for "his idea on the future of a new generation in the tropics as a painter", it "seems absolutely right to me and I continue to intend to return to it".