Shriver, 55, cited "irreconcilable differences" with her husband, whom she met in 1977 and married in 1986.
Schwarzenegger, 63, admitted in May that he had fathered a child with the family's long-time housekeeper, Mildred Baena, and announced the couple's separation.
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The niece of former US president John F. Kennedy, Shriver has asked the court for joint custody of their two younger children - Patrick, 17, and Christopher, 13 - and payment of her legal fees and alimony.
The couple has two other children: Katherine, 21, and Christina, 19.
"This has been a time of great personal and professional transition for each of us," Schwarzenegger said in a May statement to the Los Angeles Times when he and Shriver announced their separation.
"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," the statement said.
Austrian-born former bodybuilder Schwarzenegger, a liberal Republican, left office in January, and has started to return to show business, with plans for a "Governator" comic book and animated TV show.
While Arnie seems set to return to the big screen, he has vowed to pursue his political passions - notably on the environment - fueling rumors than he could even run to be the next president of the European Union.
Their marriage has come under the spotlight over the years, notably amid reports of his history of groping women during campaigning for the 2003 recall election which Schwarzenegger won, the LA Times reported.
Shriver, a former TV journalist, defended him at the time, and has stood by his side during his seven years at the helm of the Golden State, a term that ended when Jerry Brown succeeded him four months ago.
The political differences were evident during the 2008 presidential race, when Shriver backed Barack Obama and Schwarzenegger supported Republican John McCain.
