People.com broke the story Wednesday.
Anderson and Griffiths are already the parents of a son Oscar, who was born in November 2006, while Anderson also has a 13-year-old daughter, Piper, from an earlier marriage.
Anderson will soon be seen in the film "The X-Files: I Want to Believe," in which she will again play Dana Scully, a role she first played on the iconic sci-fi television show "The X-Files."
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