Advances in the realization of hybrid graphene/h-BN materials open new ways to control the electronic properties of graphene nanostructures. In this paper, the structural, electronic, and transport properties of heterojunctions made of bare zigzag-shaped h-BN and graphene ribbons are investigated using first-principles techniques. Our results highlight the potential of graphene/h-BN junctions for applications in spintronic devices. At first, density functional theory is used to detail the role played by the edge states and dangling bonds in the electronic and magnetic behavior of h-BN and graphene ribbons. Then, the electronic conductance of the junction is computed in the framework of Green’s function-based scattering theory. In its high-spin configuration, the junction reveals a full spin polarization of the propagating carriers around the Fermi energy, and the magnitude of the transmission probability is predicted to be strongly dependent on the relative orientation of magnetic momenta in the leads.