Quantum dots tuned to atomic resonances represent an emerging field of hybrid quantum systems where the advantages of quantum dots and natural atoms can be combined. Embedding quantum dots in nanowires boosts these systems with a set of powerful possibilities, such as precise positioning of the emitters, excellent photon extraction efficiency and direct electrical contacting of quantum dots. Notably, nanowire structures can be grown on silicon substrates, allowing for a straightforward integration with silicon-based photonic devices. In this work we show controlled growth of nanowire-quantum-dot structures on silicon, frequency tuned to atomic transitions. We grow GaAs quantum dots in AlGaAs nanowires with a nearly pure crystal structure and excellent optical properties. We precisely control the dimensions of quantum dots and their position inside nanowires and demonstrate that the emission wavelength can be engineered over the range of at least 30 nm around 765 nm. By applying an external magnetic field, we are able to fine-tune the emission frequency of our nanowire quantum dots to the D₂ transition of ⁸⁷Rb. We use the Rb transitions to precisely measure the actual spectral line width of the photons emitted from a nanowire quantum dot to be 9.4 ± 0.7 μeV, under nonresonant excitation. Our work brings highly desirable functionalities to quantum technologies, enabling, for instance, a realization of a quantum network, based on an arbitrary number of nanowire single-photon sources, all operating at the same frequency of an atomic transition.