The couple have been married for almost seven years and have four children together.
The news was broken by celebrity news website TMZ after months of rumours of marital difficulties.
Reports in US media suggest the reality star, 40, has requested joint legal and physical custody of their children. Neither has publicly commented.
The couple are among the most recognisable stars in the world and are both hugely successful in their own right.
Kim first found fame in 2007 as the star of an E! Television reality series about her family. Keeping up with the Kardashians has remained hugely popular since, with its 21st and final series due to air next year.
The reality star has found success in many other areas of business, from mobile apps to make-up, and Forbes estimates her personal wealth to be about $US780 million ($NZ1.06b).
Known for huge international hits like Gold Digger, Kanye West has been one of the biggest names in rap music for over 15 years. The Grammy-winning musician has also found success as a fashion designer.
The pair were friends for years before they got together and West first appeared on her family's reality show in 2010.
Their first daughter, North, arrived in June 2013.
West famously hired the San Francisco Giants' baseball stadium and an orchestra to propose to her in front of her family, and their show's cameras, later that year.
They got married in Italy in May 2014 and a photograph of them kissing on their wedding day became, at the time, Instagram's most liked post ever. By this point she and her sisters had turned social media into an art form, with their online followings propelling their business success and fame ever further.
Kardashian gave birth to the couple's first son, Saint West, the following year. They went on to have two other children, Saint and Psalm, through a surrogate after the reality star suffered from health complications during her previous pregnancies.
The couple have rarely been away from tabloid headlines since, most notably when Kardashian was robbed at gunpoint in Paris in 2016.
Last year, West unsuccessfully ran for US president. During his campaign, a series of erratic public appearances and online postings by the rapper sparked concern and led Kardashian to speak out.
She said her husband had bipolar disorder, was a "brilliant but complicated person" and called for greater empathy surrounding his mental health from the public and the media.
Rumours of their divorce have been around for months amid speculation Kardashian had hired well-known lawyer Laura Wasser.
Page Six reported the filing was imminent in January, claiming West spent the festive season away from the California-based family at his Wyoming ranch.
The wedding was the first for West and the third for Kardashian after she had brief marriages with basketball player Kris Humphries and music producer Damon Thomas.
Reuters is reporting that the divorce papers were filed a month before the March 18 premiere of the final season of Keeping Up with the Kardashians, which is expected to chronicle the recent rift in the couple's relationship.
Streaming service Hulu said in December that it had signed a deal with Kim, Khloe and Kourtney Kardashian, their mother Kris Jenner and half sisters Kylie and Kendall Jenner, in which they will create new content for a venture that is expected to debut late this year.