A picture of a tranquil young Dutchwoman pouring her morning cup of coffee is returning to the Netherlands after spending centuries in an English collection.

A Dutch Girl at Breakfast, painted by the Swiss artist Jean-Étienne Liotard in 1756, has been acquired by the Rijksmuseum in Amsterdam.

Facebook Twitter Pinterest Liotard honours Dutch Golden Age art via the painting he depicts in the background of the work. Photograph: DCMS Press Office

The British government had placed an export bar on the painting because it had been in England for so long. It was bought in 1774 by the artist’s friend and patron, the second Earl of Bessborough, and had remained in the family collection ever since.

However, no British museum could match the price of £4.4m paid by the Rijksmuseum at a Sotheby’s auction this year, so this week the export licence was granted.

Liotard, whose work was showcased in an exhibition at the Royal Academy in London last year, was a star in his day, in demand across Europe for his subtly flattering portraits.

A Dutch Girl at Breakfast is considered to be a rarity because, compared with hundreds of works in pastel, only 30 of Liotard’s oil paintings are known to have survived. This was believed to be the last in private hands.

Taco Dibbits, general director of the Rijksmuseum, said the work had the same atmosphere of peace and simplicity as Vermeer’s The Milkmaid, which the museum also owns.

“The painter allows us to get very close to his subject. As the girl carefully opens the top of the coffee pot, she won’t allow herself to be disturbed by the millions of visitors who will come to see her,” he said.

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Liotard was particularly fond of the painting, keeping it for nearly 20 years before selling it to one of his most important patrons. The artist portrayed one of his own collection of Dutch Golden Age paintings in the background of the work.

The green light for the export completes a sensational year for the Rijksmuseum, which received 2.2 million visitors and a Michelin star for its restaurant.

Another of its recent acquisitions dwarfed the sum paid for the Liotard painting: along with the Louvre in Paris, the museum bought a pair of towering portraits by Rembrandt depicting a young couple, Marten Soolmans and Oopjen Coppit, for €160m (£134m).