Representatives for the couple have confirmed that Oscar-winner Anna has given birth to the babies a few weeks earlier than expected, but that the little ones are in good health and their parents are "overjoyed".
The duo, who initially announced the pregnancy in April, waited until June to confirm that they were expecting double trouble.
Details about the birth, including the time, location and gender of the babies has not yet been revealed.
The twins are 30-year-old Anna's first children, whilst Stephen, 42, has 12-year-old Billy and 10-year-old Lilac from previous relationships.
All the news as Duchess Kate's due date draws close...