The divorce will mark the end of the couple's 25-year marriage
Maria Shriver cited irreconcilable differences for the breakup with the Terminator star, but offered no additional details.
The couple announced they had separated on May 9.
A week later, the Austrian-born former action star and ex-California governor admitted he fathered a child with Mildred Baena, a member of his household staff, years ago.

The Terminator star admitted he fathered a child with a member of household staff
Shriver's filing does state that the couple has a prenuptial agreement, which is likely to mean that Schwarzenegger's Hollywood career earnings will be evenly divided with his estranged wife.
She is seeking maintenance from him with the amount to be determined through a settlement agreement or by a judge, but details of the the divorce are expected to be handled in private.
Several of Schwarzenegger's biggest hits, including Predator, True Lies and the blockbuster sequel Terminator 2 were made during his marriage to Shriver.

Schwarzenegger's Hollywood earnings are likey to be split
Shriver was an award-winning television journalist but put her career on hold when Schwarzenegger ran for governor.
When Schwarzenegger left as California governor in January, disclosure forms showed he had at least eight interests worth $1m (£622,000) or more, although the full extent of his wealth is not known.
The forms also show that the Terminator star still retains rights to intellectual property from his days as a fitness guru and movie star.
Shriver's holdings are listed as being worth more than $1m; she is a member of the Kennedy family and is a beneficiary of some of its assets, and also owns rights and royalties from her work as an author.

Maria Shriver stood by her husband during his campaign for governor
In recent months, Shriver has appeared in videos posted on YouTube in which she talks about stress in her life, the weight of expectations and the search for faith in a troubled world.
She signed her divorce petition around two weeks ago, but her attorney filed it on Friday afternoon.
Shriver and Schwarzenegger were married in 1986 and have four children together, including two sons who are still minors.
Shriver's petition seeks joint custody of the teens, who are 17 and 13.

Arnold Schwarzenegger during his time as California' governor
She stood by her husband as he ran for California's governorship in 2003, despite reports by several women that they had been groped by the movie star.
Schwarzenegger, who later admitted he "behaved badly sometimes," was twice elected to the governorship.
He failed to fix the state's chronic budget problems and left office in January, hoping to work on environmental projects and return to the big screen.
One of his projects was an animated collaboration with comic book legend Stan Lee entitled The Governator, but the project was shelved after Schwarzenegger's admission that he had fathered the child.