Stefani filed her petition for divorce on Monday at Los Angeles Superior Court citing irreconcilable differences.
The No Doubt frontwoman married the Bush singer at a church in London's Covent Garden in September 2002 and they have three sons together.
The couple say they want joint custody of Kingston, nine, Zuma, six, and Apollo, who was born last February.
Image caption Gwen Stefani watched the US Open last year with baby Apollo
They said: "While the two of us have come to the mutual decision that we will no longer be partners in marriage, we remain partners in parenthood and are committed to jointly raising our three sons in a happy and healthy environment.
"To that end, we respectfully request privacy from the media during this time."
Image caption Gavin Rossdale and Gwen Stefani married at St Paul's, Covent Garden, in 2002 after meeting on a Bush/Goo Goo Dolls/No Doubt tour
The 45-year-old and her husband, 49, worked together on the TV talent show last year, but she later admitted it had been "awkward".
"We've only collaborated on making babies," she admitted.
The singer is also a successful designer and launched her own fashion label L.A.M.B. in 2003.
Image caption Gwen Stefani and Gavin Rossdale with their sons Zuma and Kingston at the Monsters University premiere in 2013
She wrote: "Wow #Montana u r so beautiful #favoritevacaever #neverwanttogohome."
Rossdale tweeted his 170,000 followers last Wednesday, saying: "Bye bye London. Flying home."
No date of separation was listed in the Los Angeles court filings.
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