We study stochastic gravitational waves (GWs) generated in a postinflationary magnetogenesis scenario with time-dependent gauge couplings during inflation and reheating. In this setup, magnetic anisotropic stress directly sources gravitational waves, while the induced curvature perturbations generate an additional scalar-induced GW component. We compare the spectral behavior of the two contributions and find that the magnetic-originated GW dominates the peak amplitude, whereas the scalar-induced contribution becomes important on larger scales. For $n_{\mathrm{b}}\ge 3/2$, both contributions exhibit the universal infrared scaling ${\mathrm{\Omega }}_{\mathrm{GW}}(f<f_{\mathrm{peak}})\propto f^3$, while their ultraviolet slopes differ, leading to distinct spectral signatures. For suitable reheating and magnetogenesis parameters, the resulting GW signal naturally extends into the nano-Hz range relevant for pulsar timing array observations, and it remains consistent with other bounds. The distinct spectral features of the two components may provide a useful probe of reheating dynamics and primordial magnetogenesis.

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• Cosmology
• Gravitational waves
• Primordial magnetic fields