Understanding the dynamics of species adaptation to their environments has long been a central focus of the study of evolution. Early adaptive theories proposed that populations evolve by "walking" in a fitness landscape. This "adaptive walk" is characterised by a pattern of diminishing returns, where populations further away from their fitness optimum take larger steps than those closer to their optimal conditions. This theory can also be used to understand molecular evolution in time, particularly across genes of different ages. We expect young genes to evolve faster and experience mutations with stronger fitness effects than older genes because they are further away from their fitness optimum. Testing this hypothesis, however, constitutes an arduous task. Young genes are small, encode proteins with a higher degree of intrinsic disorder, are expressed at lower levels, and are involved in species-specific adaptations. Since all these factors lead to increased protein evolutionary rates, they could be masking the effect of gene age. While controlling for these factors, we fitted models of the distribution of fitness effects to population genomic datasets of animals and plants. We found that a gene's evolutionary age significantly impacts the molecular adaptive rate. Moreover, we observed that substitutions in young genes tend to have larger fitness effects. Our study, therefore, provides the first evidence of an "adaptive walk" model of molecular evolution in large evolutionary timescales.