The British actors had been quietly dating. The wedding previously was reported by the British newspaper News of the World.
The pair costar as a married couple in the unreleased film “Dream House.”
The 43-year-old Craig had a longtime girlfriend, Satsuki Mitchell, and has a daughter from a previous relationship. The 41-year-old Weisz was in a relationship with director Darren Aronofsky (“Black Swan”), with whom she has a son.