Many established bioinks fulfill important requirements regarding fabrication standards and cytocompatibility. Current research focuses on development of functionalized bioinks with an improved support of tissue-specific cell differentiation. Many approaches primarily depend on decellularized extracellular matrices or blood components. In this study, we investigated the combination of a highly viscous alginate-methylcellulose (algMC) bioink with collagen-based artificial extracellular matrix (aECM) as a finely controllable and tailorable system composed of collagen type I (col) with and without chondroitin sulfate (CS) or sulfated hyaluronan (sHA). As an additional stabilizer, the polyphenol tannic acid (TA) was integrated into the inks. The assessment of rheological properties and printability as well as hydrogel microstructure revealed no adverse effect of the integrated components on the inks. Viability, adhesion, and proliferation of bioprinted immortalized human mesenchymal stem cells (hTERT-MSC) was improved indicating enhanced interaction with the designed microenvironment. Furthermore, chondrogenic matrix production (collagen type II and sulfated glycosaminoglycans) by primary human chondrocytes (hChon) was enhanced by aECM. Supplementing the inks with TA was required for these positive effects but caused cytotoxicity as soon as TA concentrations exceeded a certain amount. Thus, combining tailorable aECM with algMC and balanced TA addition proved to be a promising approach for promoting adhesion of immortalized stem cells and differentiation of chondrocytes in bioprinted scaffolds.