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Graphene has emerged as the foremost material for future two-dimensionalspintronics due to its tuneable electronic properties. In graphene, spininformation can be transported over long distances and, in principle, bemanipulated by using magnetic correlations or large spin-orbit coupling (SOC)induced by proximity effects. In particular, a dramatic SOC enhancement hasbeen predicted when interfacing graphene with a semiconducting transition metaldechalcogenide, such as tungsten disulphide (WS$_2$). Signatures of such anenhancement have recently been reported but the nature of the spin relaxationin these systems remains unknown. Here, we unambiguously demonstrateanisotropic spin dynamics in bilayer heterostructures comprising graphene andWS$_2$. By using out-of-plane spin precession, we show that the spin lifetimeis largest when the spins point out of the graphene plane. Moreover, we observethat the spin lifetime varies over one order of magnitude depending on the spinorientation, indicating that the strong spin-valley coupling in WS$_2$ isimprinted in the bilayer and felt by the propagating spins. These findingsprovide a rich platform to explore coupled spin-valley phenomena and offernovel spin manipulation strategies based on spin relaxation anisotropy intwo-dimensional materials.

Strongly anisotropic spin relaxation in graphene/transition metal dichalcogenide heterostructures at room temperature