Kardashian's publicist confirmed the divorce filing but did not provide further details.
The pair, who began dating in 2012 and married in a lavish ceremony in Italy two years later, rapidly became one of the world's most instantly recognisable couples.
But their union has been dogged for months by reports in the gossip press that their marriage was on the rocks as West has battled with mental health issues and launched an improbable and controversial foray into US politics.
West, 43, has opened up about his struggles with bipolar disorder.
In July last year the mercurial entertainment mogul launched a bid for the US presidency with a rambling speech during which he revealed he had wanted to abort his daughter, and broke down in tears.
He also posted a series of tweets, later deleted, that accused his wife and mother-in-law of trying to lock him up, and suggested he was seeking a divorce.
Compassion and empathy
Kardashian called on the media and public to show "compassion and empathy" following her husband's erratic behaviour.
"Those that understand mental illness or even compulsive behavior know that the family is powerless unless the member is a minor," Kardashian said in her lengthy Instagram post in July.
The couple have four children: 7-year-old daughter North, son Saint, 5, daughter Chicago, 3, and 21-month-old son Psalm.
Aside from family visits, West has been living at his sprawling ranch in Wyoming in recent months, while Kardashian and the children stayed in California.
It would be the first divorce for West and the third for Kardashian, who came to fame with the US reality TV series "Keeping Up with the Kardashians" which followed the lives of her family members in Los Angeles.
Chicago-raised rapper and record producer West has won 21 Grammys. He burst onto the rap scene on his production chops, before delivering a string of critically acclaimed studio albums, selling over 20 million copies.
He has made a very public turn to Christian evangelism in recent years, finally releasing his long-awaited gospel album.
The pair began dating in 2012 while Kardashian was going through divorce proceedings with second husband Kris Humphries.
First child North was born in June, 2013 and the couple married the following year at a 16th-century fortress in Florence, Italy after a pre-wedding celebration held at Versailles palace in France.