Single-quantum emitters are an important resource for photonic quantum technologies, constituting building blocks for single-photon sources, stationary qubits, and deterministic quantum gates. Robust implementation of such functions is achieved through systems that provide both strong light-matter interactions and a low-loss interface between emitters and optical fields. Existing platforms providing such functionality at the single-node level present steep scalability challenges. Here, we develop a heterogeneous photonic integration platform that provides such capabilities in a scalable on-chip implementation, allowing direct integration of GaAs waveguides and cavities containing self-assembled InAs/GaAs quantum dots-a mature class of solid-state quantum emitter-with low-loss Si3N4 waveguides. We demonstrate a highly efficient optical interface between Si3N4 waveguides and single-quantum dots in GaAs geometries, with performance approaching that of devices optimized for each material individually. This includes quantum dot radiative rate enhancement in microcavities, and a path for reaching the non-perturbative strong-coupling regime.Effective use of single emitters in quantum photonics requires coherent emission, strong light-matter coupling, low losses and scalable fabrication. Here, Davanco et al. stride toward this goal by hybrid on-chip integration of Si3N4 waveguides and GaAs nanophotonic geometries with InAs quantum dots.