They were found in a music book belonging to Mozart's sister Nannerl, in the foundation's archives.
Until now, all 18 scores in the music book had been attributed to Mozart's father Leopold or unknown composers.
But two compositions near the end of the book were "in all probability, bordering on certainty" the works of the young Mozart, the foundation said.
They were performed on Sunday by clavichordist Florian Birsak on Mozart's own fortepiano at the family's old Salzburg residence, for the media.
The public however will have to wait until next year to hear them live, complete with orchestrations, at the annual Mozart Week on January 22-31 in Salzburg.
The two newly discovered works were written in Leopold's hand.
"But neither the style of composition, nor the hasty correction-laden writing point to Leopold's authorship," Mozarteum researcher Ulrich Leisinger said.
"It is much more likely that Wolfgang Amadeus played the composition on the piano for his father, who then wrote it down for Wolfgang, who was still inexperienced in music writing, and later corrected it," he added.
The two pieces were unusually difficult for piano compositions at the time and their breakneck speed was not typical of Leopold's work, Leisinger also said.
"This was a young musician running riot in order to show what he was capable of," he said.
"Moreover, the piece contains real technical mistakes in composition as well as clumsy elements that never would have happened to an old hand like Leopold."
Recordings of the two pieces can be heard at www.mozarteum.at -- the website of the foundation, which aims to preserve Mozart's heritage and works, and organises regular concerts.
The scores will also be included in a printed version of Nannerl's notebook in a few months.
Mozart, born in Salzburg in 1756, began composing at the age of five and went on to produce some of the most famous concertos, symphonies and operas of his time, until his death in 1791 at the age of 35.
The latest scores are not the only ones to have resurfaced in recent years.
Last September, a library in Nantes, in western France, unveiled a previously unknown music score by Mozart that had lain in its archive undiscovered for over a century. It was authenticated by the Mozarteum.
That sheet of music was donated to the city in 1873, but was only authenticated as a Mozart work in 2007.
In 2006, a year filled with celebrations for the 250th anniversary of Austria's favourite son, another piano score extremely likely to be the work of young Wolfgang Amadeus was discovered in Salzburg.
In May last year, experts also identified three mystery musical scores discovered at the historic Jasna Gora Roman Catholic monastery in southern Poland, as possible Mozart creations.
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