Bioprinting of hydrogel-based bioinks can allow for the fabrication of elaborate, cell-laden 3D structures. In addition to providing an adequate extracellular matrix mimetic environment and high cell viability, the hydrogels must offer facile extrusion through the printing nozzle and retain the shape of the printed structure. We demonstrate a strategy to incorporate cellulose oxalate nanofibrils in hyaluronan-based hydrogels to generate shear thinning bioinks that allowed for printing of free-standing multilayer structures, covalently cross-linked after bioprinting, yielding long-term stability. The storage modulus of the hydrogels was tunable between 0.5 and 1.5 kPa. The nanocellulose containing hydrogels showed good biocompatibility, with viability of primary human dermal fibroblasts above 80% at day 7 after seeding. The cells were also shown to tolerate the printing process well, with viability above 80% 24 h after printing. We anticipate that this hydrogel system can find broad use as a bioink to produce complex geometries that can support cell growth.