Fabrication of biomimetic tissues holds much promise for the regeneration of cells or organs that are lost or damaged due to injury or disease. To enable the generation of complex, multicellular tissues on demand, the ability to design and incorporate different materials and cell types needs to be improved. Two techniques are combined: extrusion-based bioprinting, which enables printing of cell-encapsulated hydrogels; and melt electrowriting (MEW), which enables fabrication of aligned (sub)-micrometer fibers into a single-step biofabrication process. Composite structures generated by infusion of MEW fiber structures with hydrogels have resulted in mechanically and biologically competent constructs; however, their preparation involves a two-step fabrication procedure that limits freedom of design of microfiber architectures and the use of multiple materials and cell types. How convergence of MEW and extrusion-based bioprinting allows fabrication of mechanically stable constructs with the spatial distributions of different cell types without compromising cell viability and chondrogenic differentiation of mesenchymal stromal cells is demonstrated for the first time. Moreover, this converged printing approach improves freedom of design of the MEW fibers, enabling 3D fiber deposition. This is an important step toward biofabrication of voluminous and complex hierarchical structures that can better resemble the characteristics of functional biological tissues.