Conductive and stretchable materials that match the elastic moduli of biological tissue (0.5-500 kPa) are desired for bio-potential electrodes and sensors with high signal strength and stability. However, inorganic conductors and dry conducting polymers typically have elastic moduli over 1 GPa. By contrast, hydrogels made with conducting polymers are promising soft electrode materials due to their high water content. We have developed a novel method for fabricating highly conductive hydrogels comprising two interpenetrating networks: one is a connected network of the conducting polymer PEDOT:PSS, while the second affords orthogonal control over the gel’s mechanical properties. With this method, we demonstrate conductivities up to 23 S/m, a record for stretchable PEDOT:PSS-based hydrogels. Additionally, we demonstrate that the elastic modulus of the gel can be tuned over three biologically relevant orders of magnitude without compromising stretchability (>100%) or conductivity (>10 S/m).