Jude Law, 29, and his wife, actress and fashion designer Sadie Frost, 34, welcomed their third child together, a boy named Rudy Law, Tuesday night at a north London hospital, the actor's spokesman confirms to PEOPLE.com.

"They're all thrilled, " says publicist Simon Halls. "They've got three boys now."

The star of "The Talented Mr. Ripley" and "A.I.: Artificial Intelligence" left the American set of his current movie, "Cold Mountain," to be with his wife as she delivered baby Rudy, who was born five weeks prematurely and weighed 5 lbs., 5 oz. Both mother and child are said to be doing fine.

Little Rudy joins a family that already includes sister Iris, 22 months, and brothers Rafferty, 7, and Finley, 11, Frost's son from her first marriage to musician Gary Kemp of Spandau Ballet.

Law, meanwhile, is expected to rejoin the production of "Cold Mountain," which will be shooting through November. Nicole Kidman and Renee Zellweger also star.