The painting of Kate Middleton was undertaken by Paul Emsley, the 2007 winner of the Gallery's BP Portrait Award competition.
The gallery said that the duchess took part in an initial meeting to talk through the process of the painting. This was followed by two sittings, in May and June 2012, at the artist's studio in the West Country, England, and Kensington Palace.
"The Duchess explained that she would like to be portrayed naturally -- her natural self -- as opposed to her official self. She struck me as enormously open and generous and a very warm person. After initially feeling it was going to be an unsmiling portrait I think it was the right choice in the end to have her smiling -- that is really who she is," Emsley said in a statement.
The painting is due to go on show to the public Friday afternoon in London.