We demonstrate a deterministic approach to the implementation of solid-state cavity quantum electrodynamics (QED) systems based on a precise spatial and spectral overlap between a single self-assembled quantum dot and a photonic crystal membrane nanocavity. By fine-tuning nanocavity modes with a high quality factor into resonance with any given quantum dot exciton, we observed clear signatures of cavity QED (such as the Purcell effect) in all fabricated structures. This approach removes the major hindrances that had limited the application of solid-state cavity QED and enables the realization of experiments previously proposed in the context of quantum information processing.