The painting shows the princes in a casual pose wearing their military uniforms and medals.
Gallery spokesman Neil Evans said Thursday the new portrait will be on display for at least six months alongside other royal portraits.
It was painted by Nicky Philipps, a London-based artist who had the princes sit for her at her studio. She also visited Clarence House, the home of their father Prince Charles, to get the visual details she needed for the background.
In the portrait William is wearing the Queen's Golden Jubilee medal and his Order of the Garter sash and star. Harry is wearing the queen's medal and a medal awarded for his service in Afghanistan.
