During embryogenesis, organs undergo dynamic shape transformations that sculpt their final shape, composition, and function. Despite this, current organ bioprinting approaches typically employ bioinks that restrict cell‐generated morphogenetic behaviors resulting in structurally static tissues. This work introduces a novel platform that enables the bioprinting of tissues that undergo programmable and predictable 4D shape‐morphing driven by cell‐generated forces. This method utilizes embedded bioprinting to deposit collagen‐hyaluronic acid bioinks within yield‐stress granular support hydrogels that can accommodate and regulate 4D shape‐morphing through their viscoelastic properties. Importantly, precise control over 4D shape‐morphing is possible by modulating factors such as the initial print geometry, cell phenotype, bioink composition, and support hydrogel viscoelasticity. Further, shape‐morphing is found to actively sculpt cell and extracellular matrix alignment along the principal tissue axis through a stress‐avoidance mechanism. To enable predictive design of 4D shape‐morphing patterns, a finite element model is developed that accurately captures shape evolution at both the cellular and tissue levels. Finally, it is demonstrated that programmed 4D shape‐morphing enhances the structural and functional properties of iPSC‐derived heart tissues. This ability to design, predict, and program 4D shape‐morphing holds great potential for engineering organ rudiments that recapitulate morphogenetic processes to sculpt their final shape, composition, and function.