Craig's spokesman confirmed the wedding had taken place but refused to elaborate further.
Craig, 43, and Weisz, 41, have been working together on the movie The Dream House, in which they play husband and wife.
Their relationship has been very low-key.
According to the News of the World wedding guests includedCraig's 18-year-old daughter Ella and Weisz's four-year-old son Henry, together with two family friends who acted as witnesses.
A source said: “Daniel and Rachel insisted on having a small, quiet wedding. They are madly in love and couldn't wait to be husband and wife - but they wanted minimum fuss.”