Recent studies suggest increasing sensitivity to orbital variations across the Eocene-Oligocene greenhouse to icehouse climate transition. However, climate simulations and paleoenvironmental studies mostly provide snapshots of the past climate, therefore overlooking the role of this short-term variability in driving major environmental changes and possibly biasing model-data comparisons. We address this problem by performing numerical simulations describing the end-members of eccentricity, obliquity, and precession. The orbitally induced biome variability obtained in our simulations allows to reconcile previous apparent mismatch between models and paleobotanical compilations. We show that precession-driven intermittent monsoon-like climate may have taken place during the Eocene, resulting in biomes shifting from shrubland to tropical forest in the intertropical convergence zone migration region. Our Oligocene simulations suggest that, along with decreased pCO2, orbital variations crucially modulated major faunal dispersal events around the EOT such as the Grande Coupure by creating and fragmenting the biome corridors along several key land bridges.