We present a new set of period–absolute magnitude–metallicity (PMZ) relations for single-mode RR Lyrae stars calibrated for the optical GBP, V, G, GRP, near-infrared I, J, H, and Ks passbands. We compiled a large dataset (over 100 objects) of fundamental and first-overtone RR Lyrae pulsators consisting of mean intensity magnitudes, reddenings, pulsation properties, iron abundances, and parallaxes measured by the Gaia astrometric satellite in its third data release. Our newly calibrated PMZ relations encapsulate the most up-to-date ingredients in terms of both data and methodology. They are intended to be used in conjunction with large photometric surveys targeting the Galactic bulge, including the Optical Gravitational Lensing Experiment (OGLE), the Vista Variables in the Vía Láctea Survey (VVV), and the Gaia catalog. In addition, our Bayesian probabilistic approach provides accurate uncertainty estimates of the predicted absolute magnitudes of individual RR Lyrae stars. Our derived PMZ relations provide consistent results when compared to benchmark distances to globular clusters NGC 6121 (also known as M 4), NGC 5139 (also known as omega Cen), and Large and Small Magellanic Clouds, which are stellar systems rich in RR Lyrae stars. Lastly, our Ks-band PMZ relations match well with the previously published PMZ relations based on Gaia data and accurately predict the distance toward the prototype of this class of variables, the eponymic RR Lyr itself.