The introduction and control of ferromagnetism in graphene opens up a range of new directions for fundamental and applied studies. Several approaches have been pursued so far, such as introduction of defects, functionalization with adatoms, and shaping of graphene into nanoribbons with well-defined zigzag edges. A more robust and less invasive method utilizes the introduction of an exchange interaction by a ferromagnetic insulator in proximity with graphene. Here we present a direct measurement of the exchange interaction in room temperature ferromagnetic graphene. We study the spin transport in exfoliated graphene on a yttrium-iron-garnet substrate where the observed spin precession clearly indicates the presence and strength of an exchange field that is an unambiguous evidence of induced ferromagnetism. We describe the results with a modified Bloch diffusion equation and extract an average exchange field of the order of 0.2 T. Further, we demonstrate that a proximity induced 2D ferromagnet can efficiently modulate a spin current by controlling the direction of the exchange field. These results can create a building block for magnetic-gate tuneable spin transport in one-atom-thick spintronic devices.