The pistols, dated 1814, were the French emperor's last gift to his then-three-year-old heir, Sotheby's says.
The gold-encrusted pistols feature Napoleonic symbols such as the imperial eagle and the iron crown of Italy.
Napoleon was defeated in battle and sent into exile on Elba island soon after they were given.
"These remarkable treasures epitomise the greatest personal tragedy of Napoleon's life, that he saw his beloved son and heir for the last time in January 1814, destroying his hopes to create a lasting dynasty," said Christopher Mason, a specialist in European sculpture and works of art from Sotheby's.
"Within weeks the emperor had been defeated, abdicated his throne and was forced into exile on Elba. A year later he faced his final humiliation at Waterloo."
Sotheby's expects to sell the pistols for between £800,000 to £1.2m at auction on 8 July in London.
Napoleon declared himself emperor in 1804 and waged war with other European powers, conquering much of the continent.
He was finally defeated at the Battle of Waterloo in 1815 and imprisoned on the remote Atlantic island of St Helena, where he died on 5 May 1821.
His son Napoleon II, also known as the King of Rome, died of tuberculosis in 1832, at the age of 21.
A pair of pistols belonging to the son of Napoleon Bonaparte is expected to fetch up to £1.2m (1.6m euros; $1.9m) at a Sotheby's auction next month.