In this paper, we study the impact of correlation on the bit error rate (BER) and the channel capacity of a free-space optical (FSO) multiple-input-multiple-output (MIMO) system employing optical space shift keying (OSSK) over a fading channel. In order to study a practical correlated channel, we consider the effect of channel correlation due to both small-and large-scale eddies and show that the use of OSSK over correlated FSO channel can lead to an improved system performance with increasing correlation level of upto 0.9. In this work, we first develop an analytical framework for different performance metrics of the OSSK multiple-input single-output system with correlation and then extend our investigation by proposing an asymptotically accurate mathematical framework for MIMO. We also validate all the analytical results using MATLAB simulations. Finally, we develop an experimental setup of FSO with two correlated links to study the throughput and latency of the links at different turbulence levels.