Complex spatial structure, with partially isolated subpopulations, and environment heterogeneity, such as gradients in nutrients, oxygen, and drugs, both shape the evolution of natural populations. We investigate the impact of environment heterogeneity on mutant fixation in spatially structured populations with demes on the nodes of a graph. When migrations between demes are frequent, we demonstrate that environment heterogeneity can amplify natural selection and simultaneously accelerate mutant fixation and extinction, thereby fostering the quick fixation of beneficial mutants. We evidence this effect in the star graph, more strongly in the line graph, and also in a more general class of graphs. We show that for amplification to occur, mutants must have a stronger fitness advantage in demes with stronger migration outflow. In circulation graphs, where migration inflow and outflow are equal in each deme, we find that environment heterogeneity has no impact in a first approximation, but increases the fixation probability of beneficial mutants to second order. When migrations between demes are rare, we show that environment heterogeneity can also foster amplification of selection, by allowing demes with sufficient mutant advantage to become refugia for mutants.