Kate, who looked elegant as ever in a burgundy-hued Whistles dress, emerged after the viewing with Prince William looking happy and carrying what appeared to be a present. The royal couple spent ten minutes looking at the painting and meeting the artist Paul Emsley and his wife Susanne and daughter Marie before attending a private breakfast reception at the London gallery, of which Kate is patron, to mark the unveiling.
Among the guests were Kate's parents Michael and Carole Middleton and her siblings Pippa and James.
The Duchess of Cambridge, an avid art fan who herself studied history of art at St Andrew's University, was involved in the selection process, which resulted in artist Paul being chosen to paint her first official portrait. She took part in two sittings, in May and June last year, at Paul's studio in the West Country, and at Kensington Palace. He then completed the work using a series of photographs which were taken during the sittings.
Paul said he much prefered painting from photographs. "I'm always worried about the sitter - are they cold, are they hot, are they comfortable?" he said. "Photography today is so accurate and so good that it's really so much easier just to take photographs and work from them."
The painter, who was the 2007 winner of the National Portrait Gallery’s BP Portrait Award competition, first thought he would depict her without a smile. But on meeting her, he changed his mind: "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."
The 75-year-old also knew he wanted to put the focus on Kate's brunette mane. "Everyone, I think, recognises her partly through her lovely hair," he explained. "I've altered the colour of the eyes slightly to match the colour of the blouse and the blue background."
For her part, Kate told the artist's daughter during the unveiling that she "had such a fun time at the studio". Prince William was just as impressed as his wife by the painting, saying: "It's beautiful, it's absolutely beautiful."
The work took three-and-a-half months to complete using a technique of building thin layers of oil and glazes on canvas. Paul, who has also painted former South African Nelson Mandela, said of his style: "I don't have lots of things in the background. I do like large faces, I find them strong and contemporary. I'm interested in the landscape of the face, the way in which light and shadow fall across the forms. That's really my subject matter. To have anything else in there is really just an interference."
The painting, which is titled HRH The Duchess of Cambridge, will be displayed as part of the National Portrait Gallery's Contemporary Collections.