Lignin, one of the most abundant biopolymers on Earth, has been recognized as a renewable alternative to traditional petroleum-based plastics. The integration of lignin with synthetic and engineering plastics is an important approach to develop sustainable polymers. However, it is challenging to blend lignin with other polymers due to its brittle nature and poor dispersion in many composites. In order to improve the miscibility and compatibility of lignin with other plastics, a series of poly(methyl methacrylate) (PMMA) grafted lignin copolymers were prepared from atom transfer radical polymerization. The chain length of PMMA oligomers and glass transition temperature of the lignin copolymers was controlled by varying the lignin: methyl methacrylate ratio. The lignin mass fractions in the copolymers varied from 5.6% to 46.1%. These lignin–PMMA copolymers were further blended with poly(ε-caprolactone) (PCL) and engineered into nanofibrous composites by electrospinning. Tensile test and dynamical mechanical analysis showed that the incorporation of lignin–PMMA copolymers significantly improved the tensile strength, Young's modulus, and storage modulus of the resulting nanofibrous composites. The length of the PMMA chain played a crucial role in the miscibility of lignin in PCL, and therefore enhanced the stiffness and ultimate elongation of the resulting nanofibers. Cell culture studies suggested that these PCL/lignin–PMMA nanofibers were biocompatible and promoted the proliferation, attachment and interactions of human dermal fibroblasts. With reinforced mechanical properties and good biocompatibility, these green and stretchable electrospun nanofibers are potentially useful as biomaterial substrates for biomedical applications.