The exponentiated Weibull (EW) distribution has been recently proposed for the modelling of free-space optical (FSO) links in the presence of finite sized receiver aperture. In this paper, the performance of FSO communication systems over EW is studied. Specifically, the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous signal-to-noise ratio (SNR), over EW turbulence fading, are studied. The derived statistics of the SNR is utilized to analyse the performance of an FSO communication system over a generalized communication environment with turbulence induced fading, misalignment errors and path loss. New expression for the outage probability is obtained, and exact expressions for the average bit error rate (BER) are derived for various binary modulation schemes. Finally, the obtained analytical results are verified via Monte Carlo simulations.