Electroconductive hydrogels have been applied in implantable bioelectronics, tissue engineering platforms, soft actuators, and other emerging technologies. However, achieving high conductivity and mechanical robustness remains challenging. Here we report an approach to fabricating electroconductive hydrogels based on the hybrid assembly of polymeric nanofiber networks. In these hydrogels, conducting polymers self-organize into highly connected three dimensional nanostructures with an ultralow threshold (~1 wt%) for electrical percolation, assisted by templating effects from aramid nanofibers, to achieve high electronic conductivity and structural robustness without sacrificing porosity or water content. We show that a hydrogel composed of polypyrrole, aramid nanofibers and polyvinyl alcohol achieves conductivity of ~80 S cm-1, mechanical strength of ~9.4 MPa and stretchability of ~36%. We show that patterned conductive nanofiber hydrogels can be used as electrodes and interconnects with favorable electrochemical impedance and charge injection capacity for electrophysiological applications. In addition, we demonstrate that cardiomyocytes cultured on soft and conductive nanofiber hydrogel substrates exhibit spontaneous and synchronous beating, suggesting opportunities for the development of advanced implantable devices and tissue engineering technologies.