State-of-the-art quantum-well-based devices such as photovoltaics, photodetectors, and light-emission devices are enabled by understanding the nature and the exact mechanism of electronic charge transport. Ruddlesden-Popper phase halide perovskites are two-dimensional solution-processed quantum wells and have recently emerged as highly efficient semiconductors for solar cell approaching 14% in power conversion efficiency. However, further improvements will require an understanding of the charge transport mechanisms, which are currently unknown and further complicated by the presence of strongly bound excitons. Here, we unambiguously determine that dominant photocurrent collection is through electric field-assisted electron-hole pair separation and transport across the potential barriers. This is revealed by in-depth device characterization, coupled with comprehensive device modeling, which can self-consistently reproduce our experimental findings. These findings establish the fundamental guidelines for the molecular and device design for layered 2D perovskite-based photovoltaics and optoelectronic devices, and are relevant for other similar quantum-confined systems.