The club, formed in 1857 and recognised by FIFA as the oldest in the world, have sold the unique documents to raise funds for projects including the building of a new stadium.
They currently play in the Northern League, four tiers below the professional Football League.
The Sheffield laws, written some five years before the English Football Association was formed in 1863, helped to codify strands of the game that were emerging in different parts of the country.
A number of laws associated with today's game were introduced by Sheffield FC, including the indirect free-kick, the corner-kick, and the crossbar.
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