Emerging four-dimensional (4D) printing strategies offer improved alternatives to conventional three-dimensional (3D)-bioprinted structures for better compliance and simplicity of application for tissue engineering. Little is reported on simple 3D-bioprinted structures prepared by digital light processing (DLP) that can change shape-to-complex constructs (4D bioprinting) in response to cell-friendly stimuli, such as hydration. In the current research work, a bioink consisting of a blend of gelatin methacryloyl (GelMA) and poly(ethylene glycol) dimethacrylate (PEGDM) with a photoinitiator and a photoabsorber was developed and printed by DLP-based 3D bioprinting operated with visible light (405 nm). The 3D-bioprinted constructs combined with differential cross-linking due to photoabsorber-induced light attenuation were leveraged to realize structural anisotropy, which led to rapid shape deformation (as low as ≈30 min) upon hydration. The sheet thickness influenced the degree of curvature, whereas the incorporation of angled strands provided control of the deformation of the 3D-printed structure. The 4D-bioprinted gels supported the viability and proliferation of cells. Overall, this study introduces a cytocompatible bioink formulation for 4D bioprinting to yield shape-morphing, cell-laden hydrogels for tissue engineering.