We experimentally measure and characterize the channel fluctuations in a terrestrial laser communication link using spatial diversity. We measure the signals arising from the propagation of laser beams in a system that comprises two transmit and two receive apertures under various design settings. We find that the spatial channels are statistically correlated. This spatial correlation increases with receiver aperture size and with increasing proximity between beams and/or receiver apertures. By quantifying the cross-covariance between pairs of simultaneously recorded time functions, we map the spatial channel correlation of the optical wireless link as a function of beam separation at the transmitter, receiver aperture, and receiver optics separation. We discuss the effects of transverse wind velocity and establish criteria for the design of effective multiple-input multiple-output free-space optical links affected by atmospheric turbulence.