The striking image was taken at the couple's home, Windsor Castle, shortly after Easter.
It was shot by famed photographer Annie Leibovitz and is the final portrait in the series of official pictures to mark the Queen's milestone.
Her Majesty is wearing the same outfit that she wore for her other portraits, where she posed with her family including her two youngest grandchildren and her five great-grandchildren.
The close-up image shows the Queen looked perfectly relaxed next to her husband, wearing a white shirt and pink cardigan. Philip, who turned 95 on the day that the photo was unveiled, donned a quirky printed tie and smart tweed jacket.
The portrait was released at the beginning of a weekend of national and Commonwealth celebrations.
On Friday a service of thanksgiving will be held at St Paul's Cathedral followed by a lunch for the Governors General of all Commonwealth Realms at Buckingham Palace.
The Queen's official birthday will be honoured, as usual, with the annual Trooping the Colour ceremony on Saturday. Her Majesty will be joined by members of the royal family on the palace balcony as they watch an RAF flypast. In the morning, they will also observe the traditional parade.
On Sunday, the Patron's Lunch will celebrate Her Majesty's patronage of more than 600 organisations. Over 90 per cent of those organisations will be represented at the event which has been dubbed the "biggest street party" the Mall has ever seen.
Members of the public are encouraged to mirror the celebration by organising their own street parties and local fundraising events across the nation and the Commonwealth.