We develop a general pricing framework for continuously monitored geometric Asian call options for affine n-factor Gaussian diffusions and practically derive closed-form solutions for geometric Asian call options for three prominent mean-reversion commodity pricing models. In a numerical example, we examine the accuracy of our closed-form solutions via Monte Carlo (MC) simulation and use the geometric Asian call option as control variate in order to price an arithmetic Asian call option. The results confirm our closed-form solutions to be accurate and show that the MC control variate simulation approach provides a considerable variance reduction. This can be translated into substantial computation-time savings. Finally, we outline an extension to forward-start Asian options which are quite common in commodity markets. Our general approach and the presented results are neither prone to changes in model selection nor prone to changes in model parameters. Therefore, the applicability of our general pricing framework is by no means limited to the mean-reversion models or commodity markets considered within this study.