It means the boots - footwear of choice for generations of skinheads, punks and students - will join a stable of brands which also includes Hugo Boss and New Look.
The Northamptonshire-based Griggs family, who have been making shoes since 1901, will retain control of around 20% of the business.
Dr Martens employs 700 people worldwide including 350 in the UK, and its products are sold in 63 countries. The deal, expected to complete in January, will see Permira take control of parent company R Griggs.
Chief executive David Suddens said: "The brand's authenticity and the millions of customers who have used Docs as a symbol of self-expression for over half a century are what makes Dr Martens unique.
"The Permira funds respect that heritage, and want to support the management team in nurturing it."
Cheryl Potter, partner and head of the consumer sector team at Permira, said: "Dr Martens is an iconic brand with a passionate fan base of followers."
The deal follows reports of the Griggs family looking to exit the business after more than five decades running the brand that last year made £15.3 million pre-tax profits on revenues of £110 million, following an abortive sale attempt last year.
Permira is thought likely to try to expand Dr Martens' online and store presence into new international markets.
The Northamptonshire-based Griggs family have been making shoes since 1901 and started producing the Dr Martens boots in 1960 after the development of a revolutionary new air-cushioned sole by the Germans Klaus Martens and Herbert Funck.
It still pays an annual fee to the families of the two men.
The brand was a hit with a series of fashion subcultures from the skinheads and punks to the Brit Pop fans of the 1990s, but has also suffered due to changing tastes.
Production was moved to Asia but the original Northamptonshire factory was reopened in 2007 to produce vintage styles.