3D bioprinting has recently emerged as a very useful tool in tissue engineering and regenerative medicine. However, developing suitable bioinks to fabricate specific tissue constructs remains a challenging task. Herein, we report on a nanocellulose/chitosan-based bioink, which is compatible with a 3D extrusion-based bioprinting technology, to design and engineer constructs for bone tissue engineering and regeneration applications. Bioinks were prepared using thermogelling chitosan, glycerophosphate, hydroxyethyl cellulose, and cellulose nanocrystals (CNCs). Formulations were optimized by varying the concentrations of glycerophosphate (80−300 mM), hydroxyethyl cellulose (0−0.5 mg/mL), and CNCs (0−2% w/v) to promote fast gelation kinetics (<7 s) at 37 °C and retain the shape integrity of constructs post 3D bioprinting. We investigated the effect of CNCs and pre-osteoblast cells (MC3T3-E1) on the rheological properties of bioinks, bioink printability, and mechanical properties of bioprinted scaffolds. We demonstrate that the addition of CNCs and cells (5 million cells/mL) significantly improved the viscosity of bioinks and the mechanical properties of chitosan scaffolds post-fabrication. The bioinks were biocompatible and printable at an optimized range of printing pressures (12−20 kPa) that did not compromise cell viability. The presence of CNCs promoted greater osteogenesis of MC3T3-E1 cells in chitosan scaffolds as shown by the upregulation of alkaline phosphatase activity, higher calcium mineralization, and extracellular matrix formation. The versatility of this CNCs-incorporated chitosan hydrogel makes it attractive as a bioink for 3D bioprinting to engineer scaffolds for bone tissue engineering and other therapeutic applications.