The deal is a glimmer of hope in what has otherwise been a drought in European private equity deals as the region's sovereign debt crisis has driven up the cost of borrowing money for such transactions.
Some bankers had voiced concern France Telecom might abandon the sale process if bids came below expectations due to the high price of financing. European buyout deals all but ground to a halt in the second half of the year, with many pulled or postponed.
Apax, which announced the deal late on Friday, said the transaction, subject to approval by regulators, will be submitted to France Telecom's board in January.
As part of a broader portfolio review, France Telecom had been seeking to exit Switzerland where it is the third-largest player with about a 17 percent market share.
France Telecom, whose key markets aside from France are the U.K., Poland and Spain, is also trying to sell its Austrian unit. It is also reviewing operations in Africa and the Middle East as well as its enterprise unit.
The company, which received five offers in the auction of the unit, had said it hoped to reap 1.5-2 billion euros from the sale, pledging to return up to 800 million euros of the proceeds to investors via share buybacks.
France Telecom did not immediately return a phone call or an email seeking more detail on the deal, which values Orange Switzerland at 6.5 times its estimated 2011 earnings before interest, taxes, depreciation and amortisation (EBITDA).
Orange Switzerland has about 1.6 million customers, with 2010 revenues of 1.1 billion euros.
Apax said the mobile sector was a key investment area for the firm. Other investments have included Danish telecoms operator TDC
France Telecom, whose shares are down 24 percent this year, has been struggling with intensifying competition in its home market that have squeezed margins in recent quarters.
In another sign of the high capital demands it faces amid slowing growth, France Telecom earlier this week bid 891 million euros to win a block of fourth-generation mobile frequencies as part of a government auction that raised 2.6 billion euros from it and key rivals.
Nomura and Rothschild were among the banks advising on the deal, one of six buyouts with a cumulative value of 10.2 billion euros Apax was involved with this year. ($1 = 0.7669 euros)
(Reporting by Alexandria Sage and Christian Plumb; Editing by Hugh Lawson)