Abstract Background During their lifetime, microbes are exposed to environmental variations, each with its distinct spatio-temporal dynamics. Microbial communities display a remarkable degree of phenotypic plasticity, and highly-fit individuals emerge quite rapidly during microbial adaptation to novel environments. However, there exists a high variability when it comes to adaptation potential, and while adaptation occurs rapidly in certain environmental transitions, in others organisms struggle to adapt. Here, we investigate the hypothesis that the rate of evolution can both increase or decrease, depending on the similarity and complexity of the intermediate and final environments. Elucidating such dependencies paves the way towards controlling the rate and direction of evolution, which is of interest to industrial and medical applications. Results Our results show that the rate of evolution can be accelerated by evolving cell populations in sequential combinations of environments that are increasingly more complex. To quantify environmental complexity, we evaluate various information-theoretic metrics, and we provide evidence that multivariate mutual information between environmental signals in a given environment correlates well with the rate of evolution in that environment, as measured in our simulations. We find that strong positive and negative correlations between the intermediate and final environments lead to the increase of evolutionary rates, when the environmental complexity increases. Horizontal Gene Transfer is shown to further augment this acceleration, under certain conditions. Interestingly, our simulations show that weak environmental correlations lead to deceleration of evolution, regardless of environmental complexity. Further analysis of network evolution provides a mechanistic explanation of this phenomenon, as exposing cells to intermediate environments can trap the population to local neighborhoods of sub-optimal fitness.