Engineering 2D material heterostructures by combining the best of different materials in one ultimate unit can offer a plethora of opportunities in condensed matter physics. Here, in the van der Waals heterostructures of the ferromagnetic insulator Cr2Ge2Te6 and graphene, our observations indicate an out-of-plane proximity-induced ferromagnetic exchange interaction in graphene. The perpendicular magnetic anisotropy of Cr2Ge2Te6 results in significant modification of the spin transport and precession in graphene, which can be ascribed to the proximity-induced exchange interaction. Furthermore, the observation of a larger lifetime for perpendicular spins in comparison to the in-plane counterpart suggests the creation of a proximity-induced anisotropic spin texture in graphene. Our experimental results and density functional theory calculations open up opportunities for the realization of proximity-induced magnetic interactions and spin filters in 2D material heterostructures and can form the basic building blocks for future spintronic and topological quantum devices.