Michelangelo wrote some wonderful sonnets; Constable's correspondence has a fascinating tough-tenderness; most visualisers have, with varying degrees of success, tried to match words to their images. But Van Gogh's letters are the best written by any artist. Engrossing, moving, energetic and compelling, they dramatise individual genius while illuminating the creative process in general. No wonder readers have long since taken them to heart. No wonder, either, that singers have used them in their songs ("Starry Night"), and film-makers as the basis of their movies (Lust for Life). Their mixture of humble detail and heroic aspiration is quite simply life-affirming.

Received wisdom has it that the letters show Van Gogh as a tortured genius. Yet anyone who has actually read them (rather than watched the movie) will feel uncomfortable about this. There are, of course, harrowing stretches in which he frets about insanity, about poverty and about how others perceive him. But the great majority of them are impressive – even lovable – because, no matter how distressing their surrounding circumstances, they show an extraordinarily calm-sounding good sense and a beautiful directness in their account of complicated emotional states. This sense of balance, which frankly amounts to nobility, has been evident in all editions of his letters, ever since the first was published by his sister-in-law, Jo Bonger, in 1914. In this new edition it is even more vividly manifest.

The new book (or rather the new books – there are five large volumes of correspondence and a sixth of associated material) is one of the major publishing achievements of our time. It contains fresh and accurate translations of all his surviving letters (819, of which 658 are to his brother Theo) and a further 96 that he received from friends and family. Each is fastidiously annotated, which means that a sense of context is always present – no detail, however small, seems to have escaped the editors. Does this mean the main text is drowned in pedantry? No. That danger is dispelled by the large format of the volumes, and the treasure trove of illustrations: every picture Van Gogh mentions, whether it's by him or not, is reproduced, giving a virtually complete map of Van Gogh's interior world.

In its capaciousness, the book also reminds us of a fundamental truth about Van Gogh: his ambition as a painter depended on words to give it focus and direction. We see this most obviously in the correspondence with Theo. "Writing is actually an awful way to explain things to each other," he says at one point – but the exasperation here is revealingly akin to the way his paint pushes against the limits of what can be rendered and recognised as the essence of a thing. In the same way that his art often manages to make ordinary things – chairs and potatoes and sunflowers and beds – seem charged with a numinous inner life, so some of his word-descriptions catch the miraculousness of the ordinary. Writing on 31 July 1888 to Theo from Arles, he says: "I saw a magnificent and very strange effect this evening. A very large boat laden with coal on the Rhône, moored at the quay. Seen from above it was all glistening and wet from a shower; the water was a white yellow and clouded pearl-grey, the sky lilac and an orange strip in the west, the town violet. On the boat, small workmen, blue and dirty white, were coming and going. Carrying the cargo ashore. It was pure Hokusai. It was too late to do it, but one day, when this coal-boat comes back, it'll have to be tackled." The language here is more than just the counterpart to a picture. It is actually a step in the process towards the picture. It's a different kind of proof of Van Gogh's practicality – and of the way that practicality is often linked to something like exhilaration.

Exhilaration, in turn, is always either threatened or bolstered by a sense of its opposite. The story of his time in Arles with and without Gauguin is celebrated proof of this. But many of the tensions that arose during that ménage a deux had roots in Van Gogh's early life. His father's adherence to the Groningen school of theology may have opened up a pathway to the idea of divine grace being bestowed on each individual, and on the capacity for joy inherent in this idea, but it also helped to give him a moral structure that later developed distinctly oppressive aspects. As a young man in the mid 1870s, he writes: "When I think of my past life and of my father's house in that Dutch village, [I have] a feeling of 'Father, I have sinned against heaven, and in thy sight, and am no more worthy to be called thy son, make me as one of the hired servants. Be merciful to me'." Some of these religious severities troubled him until the end of his life – though others were transmuted into theories about ways of living that do and don't benefit the painting. Writing to his painter-friend Emile Bernard, he says: "I already told you last spring. Eat well, do your military drill well, don't fuck too hard; if you don't fuck too hard, your painting will be all the spunkier for it."

Right up to the day he shot himself (27 July 1890 – he died of the wound two days later), and in spite of periods of catastrophic breakdown, Van Gogh retained an exceptional capacity for careful attention to the world, and for delight arising from that attention. We can see it bravely contending with despair in very late pictures such as Wheatfield with Crows, where even the darkening sky, the ominous birds, the track vanishing into the cornfield cannot entirely obliterate the joy of its intense colours. In his final letter to Theo, which he was carrying with him on the day he shot himself, he wrote: "Ah well, I risk my life for my own work, and my reason has half foundered in it." That "half" is a vital sign.

Because this book is very expensive, not many people will be able to own it. Just as well there's a good website, on which appear all the letters written by and to Van Gogh (vangoghletters.org). Although the correspondence and its associated material have been well known and well loved for almost a century, we have never been able to enjoy them as deeply as we can now.

Andrew Motion's The Cinder Path is published by Faber.