The 15th-century portrait of a young woman holding a white ermine, a kind of short-tailed weasel, is one of just four known paintings of women by the Renaissance master. Another is the Mona Lisa.
"Ladies and gentlemen, as Polish citizens, we are now all owners of the Czartoryski collection," Culture Minister Piotr Glinski said to applause at the signing ceremony at the Royal Castle in Warsaw.
Sitting alongside him among marble columns and chandeliers and under a fresco was Prince Adam Karol Czartoryski, president of the foundation that sold the collection.
Glinski said the country paid 100 million euros (dollars) plus tax for the tens of thousands of items, "a small fraction of the market price".
In addition to the Da Vinci, which is insured for about 350 million euros ($365 million), the collection's other big names include a Rembrandt, drawings by Renoir and Chopin's letters.
When asked by reporters why he was willing to accept such a low sum, Czartoryski said: "Listen, in life you do the things the way you feel like it. I felt like making a donation and that's my choice."
The culture ministry in turn has said it wants to ensure the collection never leaves the country, which was a possibility as long as it was owned by the Princes Czartoryski Foundation.
The transaction was not without controversy, as the foundation's Polish board of directors quit last week in protest, saying the negotiations were conducted without their knowledge.
"Lady with an Ermine" is among only 15 Da Vinci paintings in the world, according to art expert Janusz Walek.
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