The modification of the surface properties of graphene with polymers provides a method for expanding its scope into new applications as a hybrid material. Unfortunately, the chemical inertness of graphene hinders the covalent functionalization required to build them up. Developing new strategies to enhance the graphene chemical activity for efficient and stable functionalization, while preserving its electronic properties, is a major challenge. We here devise a covalent functionalization method that is clean, reproducible, scalable, and technologically relevant for the synthesis of a large-scale, substrate-supported graphene-polymer hybrid material. In a first step, hydrogen-assisted plasma activation of p-aminophenol (p-AP) linker molecules produces their stable and covalent attachment to large-area graphene. Second, an in situ radical polymerization reaction of 2-hydroxyethyl acrylate (HEA) is carried out on the functionalized surface, leading to a graphene-polymer hybrid functional material. The functionalization with a hydrophilic and soft polymer modifies the hydrophobicity of graphene and might enhance its biocompatibility. We have characterized these hybrid materials by atomic force microscopy (AFM), X-Ray photoelectron spectroscopy (XPS) and Raman spectroscopy and studied their electrical response, confirming that the graphene/p-AP/PHEA architecture is anchored covalently by the sp3 hybridization and controlled polymerization reaction on graphene, retaining its suitable electronic properties. Among all the possibilities, we assess the proof of concept of this graphene-based hybrid platform as a humidity sensor. An enhanced sensitivity is obtained in comparison with pristine graphene and related materials. This functional nanoarchitecture and the two-step strategy open up future potential applications in sensors, biomaterials, or biotechnology fields.