Conductive hydrogels feature reasonable electrical performance as well as tissue-like mechanical softness, thus positioning them as promising material candidates for soft bio-integrated electronics. Despite recent advances in materials and their processing technologies, however, facile patterning and monolithic integration of functional hydrogels (e.g., conductive, low-impedance, adhesive, and insulative hydrogels) for all-hydrogel-based soft bioelectronics still poses significant challenges. Here, we report material design, fabrication, and integration strategies for an electronic-skin (e-skin) patch based on functional hydrogels. The e-skin patch was fabricated by using photolithography-compatible functional hydrogels, such as poly(2-hydroxyethyl acrylate) (PHEA) hydrogel (substrate), Ag flake hydrogel (interconnection; conductivity: ∼571.43 S/cm), poly(3,4-ethylenedioxythiophene:polystyrene) (PEDOT:PSS) hydrogel (working electrode; impedance: ∼69.84 Ω @ 1 Hz), polydopamine (PDA) hydrogel (tissue adhesive; shear strength: ∼725.1 kPa), and poly(vinyl alcohol) (PVA) hydrogel (encapsulation). The properties of these functional hydrogels closely resemble those of human tissues in terms of water content and Young's modulus, enabling stable tissue-device interfacing in dynamically changing physiological environments. We demonstrated the efficacy of the e-skin patch through its application to accelerated healing and monitoring of skin wounds in mouse models - efficient fibroblast migration, proliferation, and differentiation promoted by electric field (EF) stimulation and iontophoretic drug delivery, and monitoring of the accelerated healing process through impedance mapping. The all-hydrogel-based e-skin patch is expected to create new opportunities for various clinically-relevant tissue interfacing applications.