Neil MacGregor said the small double-sided work, depicting St Jerome on the front and with a more hastily executed painting of a comet on the back, was the first undisputed Durer to take its place in a publicly owned British collection.
He declined to give the cost of the work, which the gallery bought by private treaty from trustees of the Bacon family, but it is understood to have been between pounds 8m and pounds 10m.
Its purchase was made possible by a pounds 5m grant from the Heritage Lottery Fund and a pounds 300,000 donation from the National Art Collections Fund, an independent charity. The rest came from the National Gallery's grant-in- aid, which it saved for the purchase, and private donations.
Durer, the son of a goldsmith, was born in 1471, and brought up in Nuremberg, where he was apprenticed to a leading painter and book illustrator. The artist is particularly noted for his paintings, woodcuts and engravings.
St Jerome depicts the saint against an atmospheric, rocky landscape and a golden sunset. It has been dated to around 1495. Durer, then in his early twenties, had just made his first visit to Italy.
Characteristically, the lion, birds and landscape details are meticulously executed. St Jerome is said to have removed a thorn from a lion's paw, and here he is holding a book, presumably the Bible.
The comet on the reverse may have been included because St Jerome was supposed to have had a vision of the Last Judgment, which was to be heralded by heavenly portents.
The purchase of the painting concludes what Mr MacGregor described at the launch of the gallery's annual report yesterday as "the most remarkable year for the gallery in a long time".
In August it acquired a 15th-century Spanish masterpiece by Bartolome Bermejo, St Michael Triumphant Over The Devil With The Donor Antonio Juan, after a year of negotiations with the executors of Luton Hoo.
The painting, probably the greatest Spanish Renaissance work outside Spain, is thought to have cost pounds 10m, raised by the American Friends of the gallery from a fund endowed by John Paul Getty Jr.
More recently it acquired the most important late landscape by Georges Seurat, also with the help of a Heritage Lottery Fund grant. The 1890 Post-Impressionist masterpiece, The Channel Of Gravelines, Grand Fort- Philippe, was sold to the National by the Berggruen Collection.
Other important purchases include two oil paintings by Pierre Peyron, exemplifying the French school of neo-classicism. Belisarius Receiving Hospitality From A Peasant, 1779, and Cornelia, Mother Of The Gracchi, 1781, display superb draughtsmanship and jewel-like use of colour.Reuse content