A landscape by Vincent van Gogh is to be exhibited for the first time in more than 100 years following the discovery of crucial evidence that firmly traces back its history directly to the artist.

The significance of two handwritten numbers scribbled almost imperceptibly on the back had been overlooked until now. They have been found to correspond precisely with those on two separate lists of Van Gogh’s works drawn up by Johanna, wife of the artist’s brother, Theo.

Johanna, who was widowed in 1891 – months after Vincent’s death – singlehandedly generated interest in his art. She brought it to the attention of critics and dealers, organising exhibitions, although she obviously could never have envisaged the millions that his works would fetch today.

Le Moulin d’Alphonse Daudet à Fontvieille, which depicts vivid green grapevines leading up to a windmill with broken wings in the distance, is a work on paper that he created with graphite, reed pen and ink and watercolour shortly after he reached Arles, in the south of France.

It dates from 1888, two years before his untimely death. Windmills and vines were among his most beloved subjects.

Van Gogh, one of the greatest figures in Post-Impressionist painting, worked on paper as he excitedly awaited the arrival of his artist-friend, Paul Gauguin. He wrote to Theo that he wanted “canvas in reserve for the time when Gauguin comes”.

Research into Le Moulin d’Alphonse was conducted by James Roundell and Simon Dickinson, British art dealers, in collaboration with the Van Gogh Museum in Amsterdam.

They will be unveiling it at TEFAF Maastricht, arguably the world’s most prestigious art fair, opening in the Netherlands on Friday. They have set the price “in the region of $10m (£6.6m)”, which tallies with the figure fetched by a comparable work sold by Sotheby’s a decade ago. The vast majority are in public collections.

Roundell is a former head of Impressionist and Modern Pictures at Christie’s, whose sales of masterpieces have included Van Gogh’s Sunflowers, which broke the then record for a work of art when it sold in 1987 for nearly £25m.

Commenting on Le Moulin d’Alphonse, he said that the number “5”, in Johanna’s hand, relates to her 1902 list, while another number corresponds to her 1912 list. “So you’re getting a double reinforcement of lists that come direct from Johanna … I’m excited that we’re able to bring to light information about a drawing which really wasn’t known.”

He added: “Johanna was left with the life’s work of this artist, her brother-in-law who, in theory, she had mixed emotions about. But she set about trying to build … a legacy for him. She could have just burned the lot because, at that point, Van Gogh had no real market.”

Since its last exhibition in 1910 in Germany, the drawing – which measures 30.2 x 49 cm – has been hidden away in private European collections.

The dealers’ catalogue notes that Van Gogh arrived in Arles in 1888, exhausted and battling illness, writing to his sister that “I cannot prosper with either my work or my health in the winter”. He was immediately struck by the brilliant colours of the landscape, writing to a friend of “pale orange” sunsets, “which makes the fields appear blue”.

Most significantly, it was in Arles that Van Gogh developed as a draughtsman, producing some of his most exquisite works. In 1888, he wrote to his brother: “As for landscapes, I’m beginning to find that some, done more quickly than ever, are among the best things I do.”