Graphene has remarkable opportunities for spintronics due to its high mobility and long spin diffusion length, especially when encapsulated in hexagonal boron nitride (h-BN). Here, for the first time, we demonstrate gate-tunable spin transport in such encapsulated graphene-based spin valves with one-dimensional (1D) ferromagnetic edge contacts. An electrostatic backgate tunes the Fermi level of graphene to probe different energy levels of the spin-polarized density of states (DOS) of the 1D ferromagnetic contact, which interact through a magnetic proximity effect (MPE) that induces ferromagnetism in graphene. In contrast to conventional spin valves, where switching between high- and low-resistance configuration requires magnetization reversal by an applied magnetic field or a high-density spin-polarized current, we provide an alternative path with the gate-controlled spin inversion in graphene. The resulting tunable MPE employing a simple ferromagnetic metal holds promise for spintronic devices and to realize exotic topological states, from quantum spin Hall and quantum anomalous Hall effects, to Majorana fermions and skyrmions.