Bioelectronic interfacing with living tissues should match the biomechanical properties of biological materials to reduce damage to the tissues. Here, the authors present a fully viscoelastic microelectrode array composed of an alginate matrix and carbon-based nanomaterials encapsulated in a viscoelastic hydrogel for electrical stimulation and signal recording of heart and brain activities in vivo. Living tissues are non-linearly elastic materials that exhibit viscoelasticity and plasticity. Man-made, implantable bioelectronic arrays mainly rely on rigid or elastic encapsulation materials and stiff films of ductile metals that can be manipulated with microscopic precision to offer reliable electrical properties. In this study, we have engineered a surface microelectrode array that replaces the traditional encapsulation and conductive components with viscoelastic materials. Our array overcomes previous limitations in matching the stiffness and relaxation behaviour of soft biological tissues by using hydrogels as the outer layers. We have introduced a hydrogel-based conductor made from an ionically conductive alginate matrix enhanced with carbon nanomaterials, which provide electrical percolation even at low loading fractions. Our combination of conducting and insulating viscoelastic materials, with top-down manufacturing, allows for the fabrication of electrode arrays compatible with standard electrophysiology platforms. Our arrays intimately conform to the convoluted surface of the heart or brain cortex and offer promising bioengineering applications for recording and stimulation.