Orange Switzerland, established in 1991, employs 1,200 people.
The company had 1.6 million customers at the end of September 2011 and reported revenues of EUR1.1bn in 2010.
Gabriele Cipparrone, partner at Apax Partners, said that they have been following this asset closely over the past two years and are delighted to have secured this attractive investment opportunity.
The transaction, which is subject to the approval of the Swiss authorities, will be submitted to the board of directors of France Telecom for approval during January 2012.
Apax has completed six buyouts with a cumulative value of EUR10.2bn across the firms during 2011.