Wearable and implantable devices require conductive, stretchable and biocompatible materials. However, obtaining composites that simultaneously fulfil these requirements is challenging due to a trade-off between conductivity and stretchability. Here, we report on Ag-Au nanocomposites composed of ultralong gold-coated silver nanowires in an elastomeric block-copolymer matrix. Owing to the high aspect ratio and percolation network of the Ag-Au nanowires, the nanocomposites exhibit an optimized conductivity of 41,850 S cm-1 (maximum of 72,600 S cm-1). Phase separation in the Ag-Au nanocomposite during the solvent-drying process generates a microstructure that yields an optimized stretchability of 266% (maximum of 840%). The thick gold sheath deposited on the silver nanowire surface prevents oxidation and silver ion leaching, making the composite biocompatible and highly conductive. Using the nanocomposite, we successfully fabricate wearable and implantable soft bioelectronic devices that can be conformally integrated with human skin and swine heart for continuous electrophysiological recording, and electrical and thermal stimulation.