The appointment of Theresa May means there have been 13 UK prime ministers to serve Queen Elizabeth II.
The image was taken by celebrity photographer Annie Leibovitz and sees the Queen posing with her pet dogs.
A colour archive image shows a young Princess Elizabeth with her sister and their father, George VI.
The Queen has cancelled a visit due to gastroenteritis, a royal spokesman has said.
The Queen will join the Duke and Duchess of Cambridge in attending tomorrow's Paralympic Opening Ceremony in the Olympic Stadium.