The 27-year-old Frenchman played 29 times for Leyton Orient in 2016-17, as they were relegated from League Two.
He was out of contract, having joined the O's from Portsmouth on an 18-month deal in January 2016.
Atangana made his name in England with Havant and Waterlooville, winning their player of the year in his solitary season at Westleigh Park before joining Pompey in 2014.
He is the third close-season signing made by Cheltenham boss Gary Johnson - who himself signed a new contract on Friday - after Yeovil midfielder Kevin Dawson and Dover defender Jamie Grimes.
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Cheltenham Town have signed midfielder Nigel Atangana on a two-year deal.