The pair viewed the finished work at the University of Cambridge's Fitzwilliam Museum this week as part of their day visit to the county.
The artist admitted it had been an "extraordinary privilege" to have been chosen for the work.
He said: "It has been the most extraordinary privilege of my life to be chosen to paint this picture."
"I wanted to show Their Royal Highnesses in a manner where they appeared both relaxed and approachable, as well as elegant and dignified.
"As it is the first portrait to depict them together, and specifically during their time as the Duke and Duchess of Cambridge, I wanted the image to evoke a feeling of balance between their public and private lives.
"The piece was commissioned as a gift for the people of Cambridgeshire, and I hope they will enjoy it as much as I have enjoyed creating it."
The duke is depicted in a suit and blue tie, while the duchess donned a green Vampire's Wife dress, which was accessorised with a brooch belonging to the Queen and earrings once owned by Princess Diana.
The city of Cambridge is represented in the background with "the tones and colours of many of the historical stone buildings that are synonymous with the city" and it also features a hexagonal architectural motif which can be seen on many local buildings.
After three years on display at the museum, the portrait will be taken on a tour of local galleries and community spaces and will be loaned to the National Portrait Gallery in 2023 when the facility reopens.