In this work we demonstrate how to print 3D biomimetic hydrogel scaffolds for cartilage tissue engineering with high cell density (>107 cells ml−1), high cell viability (85 ÷ 90%) and high printing resolution (≈100 μm) through a two coaxial-needles system. The scaffolds were composed of modified biopolymers present in the extracellular matrix (ECM) of cartilage, namely gelatin methacrylamide (GelMA), chondroitin sulfate amino ethyl methacrylate (CS-AEMA) and hyaluronic acid methacrylate (HAMA). The polymers were used to prepare three photocurable bioinks with increasing degree of biomimicry: (i) GelMA, (ii) GelMA + CS-AEMA and (iii) GelMA + CS-AEMA + HAMA. Alginate was added to the bioinks as templating agent to form stable fibers during 3D printing. In all cases, bioink solutions were loaded with bone marrow-derived human mesenchymal stem cells (BM-MSCs). After printing, the samples were cultured in expansion (negative control) and chondrogenic media to evaluate the possible differentiating effect exerted by the biomimetic matrix or the synergistic effect of the matrix and chondrogenic supplements. After 7, 14, and 21 days, gene expression of the chondrogenic markers (COL2A1 and aggrecan), marker of osteogenesis (COL1A1) and marker of hypertrophy (COL10A1) were evaluated qualitatively by means of fluorescence immunocytochemistry and quantitatively by means of RT-qPCR. The observed enhanced viability and chondrogenic differentiation of BM-MSCs, as well as high robustness and accuracy of the employed deposition method, make the presented approach a valid candidate for advanced engineering of cartilage tissue.