Scalable photonic quantum information technologies require a platform combining quantum light sources, waveguides, and detectors on a single chip. Here, we introduce a van der Waals platform comprising strain-engineered bilayer WSe₂ quantum emitters, integrated on multimode WS₂ waveguides with grating couplers, enabling efficient on-chip quantum light sources. The emitters exhibit bright, highly polarised emission that couples efficiently into WS₂ waveguides. Under discrete-state excitation, we observe high-purity, waveguide-coupled single-photon emission, measured using both single-port and cross-correlated, multi-port photon streams, yielding g⁽²⁾(0) = 0.003^(+0.030)_(-0.003) and g⁽²⁾(0) = 0.076±0.023, respectively. For a single output, the out-coupled single-photon count rate at the first lens reaches approximately 357 kHz under continuous-wave discrete-state excitation, corresponding to an estimated minimum waveguide-coupled rate of 1.68 MHz. These results demonstrate an efficient, integrated single-photon source and establish a pathway toward scalable photonic quantum information processing centred around nanoengineered van der Waals materials.