People magazine said Craig, 43, and Weisz, 41, were married in a secret ceremony Wednesday attended by just four people -- Craig's daughter Ella, 18; Weisz's son Henry, 4; and two friends.
Britain's Daily Mail said the two were last seen together in London in March on a shopping spree at the Louis Vuitton store in Mayfair.
The actors play husband and wife in the upcoming horror movie "The Dream House" and while they have been friends for several years, they denied they were a couple when they were first linked by reports in November, the Daily Mail reported.
Weisz had a relationship with "Black Swan" director Darren Aronofsky for nine years before getting together with Craig, who was engaged to Satsuki Mitchell for five years.
"The Dream House" opens in theaters in September.
Craig is gearing up for the release of the Hollywood remake of "The Girl with the Dragon Tattoo" and he returns as the legendary spy James Bond in the 23rd movie in the series.
The Daily Mail said the Bond sequel has been delayed because of financial problems and no release date has been set.