Displayed on the sidelines of the Salzburg Festival in Mozart's birthplace, the 12-page manuscript is a transcription in the young composer's hand of the Stabat Mater -- a Marian hymn -- by Italian master of counterpoint Eugenio di Ligniville.
The manuscript, sold at the London auction in May by a private individual, also bears annotations by the child prodigy's father Leopold.
Experts date the manuscript to 1773, when Wolfgang Amadeus Mozart was 17.
"It is one of the most impressive single manuscripts arising from Mozart's concentrated canonic and contrapuntal studies in Salzburg between 1772 and 1774," Sotheby's said in its description of the lot.
"Mozart probably came across the (piece) when he met the composer in April 1770 in Florence during his first Italian journey," Sotheby's said.
At the time, Ligniville was director of music at the court of Tuscany, the auction house said, adding that Leopold Mozart described Ligniville as "the finest expert in counterpoint in the whole of Italy".
Leopold Mozart "recorded that he 'placed the most difficult fugues before Wolfgang and gave him the most difficult themes, which he played off and worked out as easily as one eats a piece of bread'," Sotheby's said.
The Salzburg Mozarteum Foundation, which houses more than half of the known manuscripts of the Mozart family, said the acquisition of the latest manuscript was made possible by a donation.
"Most of Mozart's manuscripts have long been held in collections that are accessible by the public, but a small handful of them remain inaccessible to experts," the non-profit foundation said in a statement.