Financial details of the deal were not revealed.
As part of the agreement, Permira announced plans to reinforce K-Way’s brand leadership in France and Italy, as well as expand its product range and store portfolio, with a focus on international growth.
Permira principal and head of France Sebastien Floch said: "We have followed the business for a number of years and have found that K-Way is a brand with real scarcity value, which encompasses everything the Permira Consumer team loves to back: an iconic brand and product, strong heritage and DNA, universal customer appeal and distinctive positioning.
"We look forward to bringing our experience and resources to the table to support K-Way's continued success and its global expansion plans.”
Permira acquired Dr Martens from the Griggs family in January 2014 for £300m. It also owns Italian luxury sneaker brand Golden Goose, which it bought for €1.28bn (£1.09m) in 2020.