Van der Waals heterostructures show many intriguing phenomena including ultrafast charge separation following strong excitonic absorption in the visible spectral range. However, despite the enormous potential for future applications in the field of optoelectronics, the underlying microscopic mechanism remains controversial. Here we use time- and angle-resolved photoemission spectroscopy combined with microscopic many-particle theory to reveal the relevant microscopic charge transfer channels in epitaxial WS_{2}/graphene heterostructures. We find that the timescale for efficient ultrafast charge separation in the material is determined by direct tunneling at those points in the Brillouin zone where WS_{2} and graphene bands cross, while the lifetime of the charge separated transient state is set by defect-assisted tunneling through localized sulphur vacancies. The subtle interplay of intrinsic and defect-related charge transfer channels revealed in the present work can be exploited for the design of highly efficient light harvesting and detecting devices.