We propose that cosmological magnetic fields generated in regions of finite spatial dimensions may manifest themselves in the global dynamics of the Universe as `dark energy'. We test our model in the context of spatially flat cosmological models by assuming that the Universe contains non-relativistic matter $\rho_m\propto \alpha^{-3}$, dark energy $\rho_{Q}\propto \alpha^{-3(1+w)}$, and an extra fluid with $\rho_{B} \propto \alpha^{n-3}$ that corresponds to the magnetic field. We place constraints on the main cosmological parameters of our model by combining the recent supernovae type Ia data and the differential ages of passively evolving galaxies. In particular, we find that the model which best reproduces the observational data when $\Omega_m=0.26$ is one with $\Omega_{B}\simeq 0.03$, $n\simeq 7.68$, $\Omega_{Q}\simeq 0.71$ and $w\simeq -0.8$.