The performance of free-space optical (FSO) communication systems based on avalanche photodiodes (APDs) is investigated over the aggregated double generalized gamma (double GG) fading channels. The approximate average bit error rate (ABER) expression is theoretically derived in terms of the double GG distributions under moderate and strong turbulent atmospheric conditions considering thermal noise and shot noise. The union bound and Hermite polynomials are then used to estimate the ABER performance of M-ary pulse-position modulation (PPM)-based systems and orthogonal frequency division multiplexing scheme (OFDM)-based systems. The ABER performance is studied with different receiver noise temperatures, modulation orders, turbulence strengths, and average photon counts assuming plane wave and spherical wave propagations. The results show that adopting an optimal average APD gain affected by the receiver temperature minimizes the ABER value for both wave propagations. In addition, the present APD-based system offers better ABER performance than that of a PIN-based FSO system over the double GG fading channels at two receiver noise temperatures of 200 and 400 K for both the PPM and OFDM schemes. We provide a reference for FSO system design.