Many photonic quantum information processing applications would benefit from a high brightness, fiber-coupled source of triggered single photons. Here, we present a fiber-coupled photonic-crystal waveguide (PCWG) singlephoton source relying on evanescent coupling of the light field from a tapered outcoupler to an optical fiber. A two-step approach is taken where the performance of the tapered outcoupler is recorded first on an independent device containing an on-chip reflector. Reflection measurements establish that the chip-to-fiber coupling efficiency exceeds 80%. The detailed characterization of a high-efficiency PCWG extended with a tapered outcoupling section is then performed. The corresponding overall single-photon source efficiency is 10.9%±2.3%, which quantifies the success probability to prepare an exciton in the quantum dot, couple it out as a photon in the waveguide, and subsequently transfer it to the fiber. The applied outcoupling method is robust, stable over time, and broadband over several tens of nanometers, which makes it a highly promising pathway to increase the efficiency and reliability of planar chip-based single-photon sources.