The black-and-white, hand-stitched silk stockings with crests are believed to have been her favourite design in the 1870s.
They were sold yesterday by Lyon & Turnbull at an auction.
It is understood the royal stockings went to a private collector. Lee Young of Lyon & Turnbull said: "The stockings were bought by a dealer on behalf of a third party. When I was shown the stockings I was immediately reminded of a scene in the film The Young Victoria, where Prince Albert knelt at Queen Victoria's feet and rolled her silk stockings up her legs. It contradicts the image we usually have of the Queen as a rather large elderly lady dressed in black."
Mr Young added: "Examples of the Queen's undergarments have long been the crowning glory for Victoriana collectors around the world. In the past few years several items have come up for auction and made excellent prices, with interest from around the world."
The Queen's undergarments, along with the much of her wardrobe, were distributed to members of the royal household upon the monarch's 1901 death.
Other items of note in the sale included Napoleon's favourite pipe, which went for 4,000. Carved with his double eagle crest, it came with a handwritten note stating it was purchased at the sale of his affects in St Helena, 1821.
The auction also saw a pair of Chelsea Finger Bowls and Stands sell for 27,500 and a Chinese porcelain horse sell for 21,250.