Van der Waals heterostructures (vdWHSs) provide a unique playground to study fundamental physics and practical applications of two-dimensional (2D) materials. However, most 2D heterostructures are prepared by transfer, hindering their technological implementation. Here, we report the first chemical vapour deposition of monolayered MoS2/WS2/graphene vertical vdWHS without transfer step. By atomic force microscopy, photoluminescence, Raman spectroscopy, and secondary ion mass spectroscopy, we confirmed the vertical stacking of three different 2D materials. The use of WS2, graphene, and sapphire as growth substrates allowed us to describe the 2D materials growth process better. We determined that for the synthesis of 2D materials, only the chemical potential of the crystal formation and the substrate-layer adhesion energy are relevant factors. In addition, we used MoS2/WS2/graphene vdWHS to fabricate a photoresponsive memory device, showing the application potential of such heterostacks. Our results clarify the growth mechanisms of 2D materials and pave the way for the growth of more complex vdWHSs.