-In this paper, we presented the ergodic capacity of free space optical communication systems over Gamma-Gamma atmospheric turbulence fading channels with perfect channel state information for the developed system. The intensity fluctuations of the received optical signal are accounted for Gamma-Gamma atmospheric turbulence. A closed-form expression for the average capacity of the heterodyne differential phase shift keying for free-space optical (FSO) communication systems over gamma-gamma turbulence channel is derived.