A large enhancement in the spin–orbit coupling of graphene has been predicted when interfacing it with semiconducting transition metal dichalcogenides. Signatures of such an enhancement have been reported, but the nature of the spin relaxation in these systems remains unknown. Here, we unambiguously demonstrate anisotropic spin dynamics in bilayer heterostructures comprising graphene and tungsten or molybdenum disulphide (WS2, MoS2). We observe that the spin lifetime varies over one order of magnitude depending on the spin orientation, being largest when the spins point out of the graphene plane. This indicates that the strong spin–valley coupling in the transition metal dichalcogenide is imprinted in the bilayer and felt by the propagating spins. These findings provide a rich platform to explore coupled spin–valley phenomena and offer novel spin manipulation strategies based on spin relaxation anisotropy in two-dimensional materials.