The statistical properties of the multivariate GammaGamma (ΓΓ) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF), cumulative distribution function (CDF) and moment generation function of the multivariate ΓΓ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the su m of ΓΓ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.