We present the first model of full-sky polarized synchrotron emission that is derived from all WMAP and Planck LFI frequency maps. The basis of this analysis is the set of end-to-end reprocessed COSMOGLOBE Data Release 1 (DR1) sky maps presented in a companion paper, which have significantly lower instrumental systematics than the legacy products from each experiment. We find that the resulting polarized synchrotron amplitude map has an average noise rms per 2° full width at half maximum (FWHM) beam of 3.2 μK at 30 GHz. This is 30% lower than the recently released BEYONDPLANCK model that included only LFI+WMAP Ka–V data, and 29% lower than the WMAP K-band map alone. The mean B-to-E power spectrum ratio is 0.39 ± 0.02, with amplitudes consistent with those measured previously by Planck and QUIJOTE. Assuming a power law model for the synchrotron spectral energy distribution and using the T–T plot method, we find a full-sky inverse noise-variance-weighted mean of the synchrotron polarized spectral index of βs = −3.07 ± 0.07 from the COSMOGLOBE DR1 K band and 30 GHz, in good agreement with previous estimates. In summary, the novel COSMOGLOBE DR1 synchrotron model is both more sensitive and systematically cleaner than similar previous models, and it has a more complete error description that is defined by a set of Monte Carlo posterior samples. We believe that these products are preferable over previous Planck and WMAP products for all synchrotron-related scientific applications, including simulations, forecasting, and component separation.