The British firm, which was put up for sale in April, had attracted attention from a number of suitors.
As well as shoes, Jimmy Choo produces a range of luxury goods.
Jimmy Choo shoes featured the 90s TV hit show, Sex and the City, and are still seen on the feet of the famous, including the Duchess of Cambridge, Beyonce and Kendal Jenner.
"Some other brands are very over exposed, like the red-soled Loubutin, but Jimmy Choo managed to get in the limelight, stay there but never become over saturated," said Lisa Armstrong, fashion director of the Daily Telegraph.
Malaysian-born Jimmy Choo trained at the renowned Cordwainers Technical College in London.
He founded the business in 1996 with former Vogue journalist Tamara Mellon.
In 2001 Ms Mellon and private equity investors bought out Mr Choo.
Ten years later, Ms Mellon left the business to launch her own clothing line.
In 2014, Jimmy Choo listed on the London Stock Exchange, by which time JAB, owned by the German billionaire Reimann family, was the main shareholder.
JAB Holdings is backing this deal.
The Telegraph's Lisa Armstrong says that Jimmy Choo feels this deal with fellow fashion house Michael Kors is better than being "passed around by more venture capitalists".
Michael Kors describes itself as a luxury brand, and, like Jimmy Choo, it is named after its founder and creative force.
Its handbags are priced at between $200-600 (£160-460).
Recent years have been a struggle for the company, its most recent same-store sales figures were down 14%.
Michael Kors said the acquisition was expected to deliver a number of benefits, including "the opportunity to grow Jimmy Choo sales to one billion dollars" and "a more balanced portfolio with greater product diversification".
It said Jimmy Choo would also have the opportunity to grow in the men's luxury footwear category, as well as greater exposure to global markets, "particularly the fast-growing market in Asia".