The painting by Jamie Coreth shows the Duke of Cambridge, second in line to the throne behind his father Prince Charles, in a dark suit and the Duchess wearing a long emerald dress.
The artist said: "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."
Prince William and Kate were able to see the portrait on Thursday on a visit to Cambridge, where it is on public display at the university’s Fitzwilliam Museum. It will be briefly lent to the National Portrait Gallery in London next year.
The Duke praised Coreth's work, telling him it was "amazing" and commenting on its size, describing it as "quite big".
The portrait was commissioned by the Cambridgeshire Royal Portrait Fund and Coreth deliberately chose a background palette redolent of the many historic stone buildings of Cambridge.
Last week Prince William was out on the streets of London to help sell copies of The Big Issue magazine for the eponymous homeless charity.
And on Wednesday, the Duke and his wife were in attendance for the unveiling of a statue commemorating the achievements of the Windrush generation of immigrants, at Waterloo Station in London.
The previous day Prince William turned 40, with some commentators suggesting he will play an even greater role in the UK's royal family in the years to come.