Heterostructures involving two-dimensional (2D) transition metal dichalcogenides and other materials such as graphene have a strong potential to be the fundamental building block of many electronic and opto-electronic applications. The integration and scalable fabrication of such heterostructures is of essence in unleashing the potential of these materials in new technologies. For the first time, we demonstrate the growth of few-layer MoS2 films on graphene via non-aqueous electrodeposition. Through methods such as scanning and transmission electron microscopy, atomic force microscopy, Raman spectroscopy, energy and wavelength dispersive X-ray spectroscopies and X-ray photoelectron spectroscopy, we show that this deposition method can produce large-area MoS2 films with high quality and uniformity over graphene. We reveal the potential of these heterostructures by measuring the photo-induced current through the film. These results pave the way towards developing the electrodeposition method for the large-scale growth of heterostructures consisting of varying 2D materials for many applications.