The Los Angeles Times reported Monday Shriver moved out of the couple's home in Brentwood, Calif., a few weeks ago and the two issued a joint statement confirming they had separated.
"This has been a time of great personal and professional transition for each of us," the statement said. "After a great deal of thought, reflection, discussion and prayer, we came to this decision together. At this time, we are living apart while we work on the future of our relationship.
"We are continuing to parent our four children together. They are the light and the center of both of our lives," Schwarzenegger and Shriver said.
The statement indicated the former power couple regard their separation as "a private matter and neither we nor any of our friends or family will have further comment."
"We ask for compassion and respect from the media and the public."
Schwarzenegger has indicated he plans to go back to work as a movie actor, after serving as governor. Shriver continues to work in TV journalism.
DISCUSS AND COMMENT ON THIS STORY Reality TV World now offers Facebook Comments on our stories. To post a comment, log into Facebook and then 'Add' your comment. To report spam or abuse, click the 'X' in the upper right corner of the comment box.