The outfit, which is made up of a black silk taffeta, bombazine bodice and matching grosgrain skirt with a 43-inch waist, was expected to sell for between 1,000 and 2,000 pounds.
But with bidding starting at 2,000 pounds, the outfit finally sold for 6,200 pounds to an American buyer at the auction at Hansons Derbyshire Auction Centre in Etwall, Derbyshire.
A fine black straw hat with mourning veil mounted with a shining ostrich feather also comes with the costume, the Daily Mail reported.
The royal family's milliner Robert Heath of Hyde Park Corner designed and made the complete set for the monarch, which also comes with a pair of small black boots and monogrammed silk undergarments.
The royal attire was consigned to the auctioneers after being purchased in a house sale in the 1970s.
Following the auction, a spokeswoman at Hansons Auctioneers said: "The sale went extremely well. There was a very good atmosphere and the dress will now be making its way to the US."
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Queen Victoria, was Britain's longest reigning monarch, ruling from June 1837 until January 1901.
She remained in mourning until the end of her life after her husband Albert died suddenly of typhoid in December 1861, aged 42.