The couple have been married for more than 25 years and are the parents of four children.
Shortly after they confirmed in May they had separated this year, Schwarzenegger admitted he had fathered a son with a member of his household staff more than a decade earlier.
UsMagazine.com said Shriver cited "irreconcilable differences" as the reason she was seeking to divorce her husband.
Shriver requested joint legal and physical custody of her sons with Schwarzenegger -- Patrick, 17, and Christopher, 13, the report said.
The couple's other two children are over the age of 18.
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