Soft tissues are commonly fiber-reinforced hydrogel composite structures, distinguishable from hard tissues by their low mineral and high water content. In this work, we proposed the development of 3D printed hydrogel constructs of the biopolymers chitosan (CHI) and cellulose nanofibers (CNFs), both without any chemical modification, which processing did not incorporate any chemical crosslinking. The unique mechanical properties of native cellulose nanofibers offer new strategies for the design of environmentally friendly high mechanical performance composites. In the here proposed 3D printed bioinspired CNF-filled CHI hydrogel biomaterials, the chitosan serves as a biocompatible matrix promoting cell growth with balanced hydrophilic properties, while the CNFs provide mechanical reinforcement to the CHI-based hydrogel. By means of extrusion-based printing (EBB), the design and development of 3D functional hydrogel scaffolds was achieved by using low concentrations of chitosan (2.0–3.0% (w/v)) and cellulose nanofibers (0.2–0.4% (w/v)). CHI/CNF printed hydrogels with good mechanical performance (Young’s modulus 3.0 MPa, stress at break 1.5 MPa, and strain at break 75%), anisotropic microstructure and suitable biological response, were achieved. The CHI/CNF composition and processing parameters were optimized in terms of 3D printability, resolution, and quality of the constructs (microstructure and mechanical properties), resulting in good cell viability. This work allows expanding the library of the so far used biopolymer compositions for 3D printing of mechanically performant hydrogel constructs, purely based in the natural polymers chitosan and cellulose, offering new perspectives in the engineering of mechanically demanding hydrogel tissues like intervertebral disc (IVD), cartilage, meniscus, among others.