Superconductivity and magnetism are two antagonistic cooperative phenomena, and the intriguing problem of their coexistence has been studied for several decades. Recently, artificial hybrid superconductor-ferromagnet systems have been commonly used as model systems to reveal the interplay between competing superconducting and magnetic order parameters, and to verify the existence of new physical phenomena, including the predicted domain-wall superconductivity (DWS). Here we report the experimental observation of DWS in superconductor-ferromagnet hybrids using a niobium film on a BaFe(12)O(19) single crystal. We found that the critical temperature T(c) of the superconductivity nucleation in niobium increases with increasing field until it reaches the saturation field of BaFe(12)O(19). In accordance with the field-shift of the maximum value of T(c), pronounced hysteresis effects have been found in resistive transitions. We argue that the compensation of the applied field by the stray fields of the magnetic domains as well as the change in the domain structure is responsible for the appearance of the DWS and the coexistence of superconductivity and magnetism in the superconductor-ferromagnet hybrids.