The affordable fashion brand, known for its handbag range, will change its name to Capri Holdings once the deal has closed, the firm said.
John D. Idol, chairman and chief executive officer of Michael Kors Holdings, said the deal was “an important milestone for our group”.
“For over 40 years, Versace has represented the epitome of Italian fashion luxury, a testament to the brand’s timeless heritage.
"We are excited to have Versace as part of our family of luxury brands, and we are committed to investing in its growth,” he said.
“With the full resources of our group, we believe that Versace will grow to over $2bn in revenues.
"We believe that the strength of the Michael Kors and Jimmy Choo brands, and the acquisition of Versace, position us to deliver multiple years of revenue and earnings growth.”
Confirmation of the sale comes after fans called on Versace to put a stop to the sale.
The Italian luxury brand was founded by Gianni Versace 40 years ago. After Mr Versace was murdered in 1997, his family took over the company.
The Versace family currently have an 80 per cent stake in the company, while the remaining 20 per cent is held by private equity group Blackstone, which bought into the firm in 2014, with plans to list it on the stock market.
However, Blackstone is reported to have found the investment disappointing, and abandoned its plans for a float some time ago.
Donatella Versace, the group’s vice president and chief designer, said: “This is a very exciting moment for Versace. It has been more than 20 years since I took over the company along with my brother Santo and daughter Allegra. I am proud that Versace remains very strong in both fashion and modern culture.
“Versace is not only synonymous with its iconic and unmistakable style, but with being inclusive and embracing of diversity, as well as empowering people to express themselves. Santo, Allegra and I recognize that this next step will allow Versace to reach its full potential.”
Ms Versace added: “We believe that being part of this group is essential to Versace’s long-term success. My passion has never been stronger. This is the perfect time for our company, which puts creativity and innovation at the core of all of its actions, to grow.
“Santo, Allegra and I will become shareholders in Capri Holdings. This demonstrates our belief in the long-term success of Versace and commitment to this new global fashion luxury group.”
The purchase of Versace is the second major deal announced by Michael Kors in the last 18 months - the company bought shoe designer Jimmy Choo for £921m last year.
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