3D bioprinting is usually implemented on flat surfaces, posing serious limitations in the fabrication of multilayered curved constructs. 4D bioprinting, combining 3D bioprinting with time-dependent stimuli-induced transformation, enables the fabrication of shape-changing constructs. Here, a 4D biofabrication method is reported for cartilage engineering based on the differential swelling of a smart multi-material system made from two hydrogel-based materials: hyaluronan and alginate. Two ink formulations are used: tyramine-functionalized hyaluronan (HAT, high-swelling) and alginate with HAT (AHAT, low-swelling). Both inks have similar elastic, shear-thinning, and printability behavior. The inks are 3D printed into a bilayered scaffold before triggering the shape-change by using liquid immersion as stimulus. In time (4D), the differential swelling between the two zones leads to the scaffold’s self-bending. Different designs are made to tune the radius of curvature and shape. A bioprinted formulation of AHAT and human bone marrow cells demonstrates high cell viability. After 28 days in chondrogenic medium, the curvature is clearly present while cartilage-like matrix production is visible on histology. A proof-of-concept of the recently emerged technology of 4D bioprinting with a specific application for the design of curved structures potentially mimicking the curvature and multilayer cellular nature of native cartilage is demonstrated.