Gelatin/chitosan hydrogels have attracted considerable attention over the last 2 decades in various fields of applications. In this paper, chemically crosslinked composite hydrogels with different gelatin-to-chitosan weight ratios were fabricated and crosslinked with different amounts of genipin via the solvent casting technique combined with freeze-drying. Fourier-transform infrared, scanning electron microscopy (SEM), liquid displacement method, and gravimetric analysis were used to examine the chemical, microstructural, and physical properties of the hydrogels. IR spectra confirmed the formation of covalent bonds between the amino groups of the parent's macromolecules and genipin. SEM micrographs indicated that the hydrogels possessed a highly porous structure with well-defined pore geometries. The swelling capacity and degradation rate of the specimens reduced with increasing the amounts of chitosan and/or genipin. In-depth swelling measurements revealed that the first-order kinetic model was only applicable in the early stage of the swelling study; however, the water absorption behavior of the hydrogels was best described by the pseudo-second-order kinetic model (Schott's model) throughout the swelling experiment. The genipin-crosslinked hydrogels were found to support MC3T3-E1 cell proliferation. The results of this paper thus suggest the 1.5% genipin-crosslinked gelatin/chitosan hydrogels as promising candidates for on-demand drug delivery applications or more precisely osteoarthritis drug delivery systems.