The performance of a ground-station-to-space laser uplink with a Gaussian-beam wave model subject to turbulence and beam wander effects is the topic of the present study. The modulated gamma distribution is used to describe the combined effect of the above two deteriorating factors. At first, a versatile expression of the above probability density function is deduced. We then derive novel closed-form expressions for its cumulative distribution function and the moment-generating function. The scintillation index and the probability of fade are hence readily evaluated. The analysis is completed with the evaluation of the bit error rate assuming heterodyne detection with differential phase-shift keying. In order to attain an adequate error rate target, we incorporate diversity at the satellite receiver. A proper simulation scenario is adopted, and numerical results are provided to verify the accuracy of the derived expressions.