The colorful screenprints are based on a formal photograph of the queen wearing a tiara and necklace that was used during her Silver Jubilee celebrations in 1977.
They will form part of the Portraits of a Monarch exhibit starting in November at Windsor Castle. The purchase was announced Monday, but royal officials refused to say how much was paid for the portraits.
The purchase brings the distinctive style of the American artist to a collection of portraits of British rulers that dates back to the 15th Century.
"They are in a very interesting and contemporary technique that Andy Warhol really popularized, screen printing with wonderfully vibrant colors, in multiples," said Royal Librarian Jane Roberts. "They join a collection dating back 4, 5, 600 years. The fact that they are in a completely new technique is not surprising; things change."
Roberts said the queen had approved the purchase.
"The Warhol prints of the queen are in many ways the most important popular image of the queen to be created by an artist print maker over the last few decades," she said.
Warhol, who died in 1987, was one of the most commercially successful artists of the 20th Century and used similar techniques in portraits of Marilyn Monroe, Jackie Kennedy, and Elvis Presley. He created these images of the queen in 1985 as part of a portfolio of screenprints called "Reigning Queens."
The exhibit will be open to people who visit Windsor Castle, which is roughly 20 miles west of London. It will run until June 2013.