This paper studies the multivariate Ricean distribution, which is the most important distribution for modeling the magnitude of the received signal when line-of-sight propagation conditions exist. In this paper, assuming different mean values for the Ricean distributed random variables, generic expressions for the multivariate Ricean probability density function, cumulative distribution function, and the joint moments are derived in terms of integral representations. As an application example, these results have been used to analyze the performance of a multi-branch selection diversity receiver, operating in spatially correlated Ricean fading environment. Moreover, an asymptotic closed-form expression has been also provided, which approximates quite well to the exact one, and has been used to study various performance metrics. Finally, a complexity analysis has been performed and simulation results have been also presented.