The manufacturing of modern scaffolds with customized geometry and personalization has become possible due to the three-dimensional (3D) printing technique. A novel type of 3D-printed scaffolds for bone tissue regeneration based on poly(ε-caprolactone) (PCL) filled with nanocrystalline cellulose modified by poly(glutamic acid) (PGlu-NCC) has been proposed in this study. The 3D printing set-ups were optimized in order to obtain homogeneous porous scaffolds. Both polymer composites and manufactured 3D scaffolds have demonstrated mechanical properties suitable for a human trabecular bone. Compression moduli were in the range of 334–396 MPa for non-porous PCL and PCL-based composites, and 101–122 MPa for porous scaffolds made of the same materials. In vitro mineralization study with the use of human mesenchymal stem cells (hMSCs) revealed the larger Ca deposits on the surface of PCL/PGlu-NCC composite scaffolds. Implantation of the developed 3D scaffolds into femur of the rabbits was carried out to observe close and delayed effects. The histological analysis showed the lowest content of immune cells and thin fibrous capsule, revealing low toxicity of the PCL/PGlu-NCC scaffolds seeded with rabbit MSCs (rMSCs) to the surrounding tissues. The most pronounced result on the generation of new bone tissue after implantation of PCL/PGlu-NCC + rMSCs scaffolds was detected by both microcomputed tomography and histological analysis. Around 33% and 55% of bone coverage were detected for composite 3D scaffolds with adhered rMSCs after 1 and 3 months of implantation, respectively. This achievement can be a result of synergistic effect of PGlu, which attracts calcium ions, and stem cells with osteogenic potential.