Diversity reception can be used over free-space optical links to mitigate atmospheric turbulence effects on system performance. In this paper, we present the error rate analysis for equal gain combining with heterodyne detection in coherent free-space optical communication systems over K-distributed atmospheric turbulence channels. The signal-to-noise ratio statistics of the combiner output are analyzed, and a new closed-form characteristic function is derived for the square root of instantaneous signal-to-noise ratio. Based on this characteristic function, error rates for binary phase-shift keying and outage probability are presented for equal gain combining schemes. Comparing to the maximum ratio and selection diversity reception techniques, our results demonstrate the usefulness of equal gain combining reception in coherent free-space optical communications. Simulation results are presented to further verify the accuracy of the analytical results.