Although three-dimensional (3D) bioprinting technology is rapidly developing, the design strategies for biocompatible 3D-printable bioinks remain a challenge. In this study, we developed a machine learning-based method to design 3D-printable bioink using a model system with naturally derived biomaterials. First, we demonstrated that atelocollagen (AC) has desirable physical properties for printing compared to native collagen (NC). AC gel exhibited weakly elastic and temperature-responsive reversible behavior forming a soft cream-like structure with low yield stress, whereas NC gel showed highly crosslinked and temperature-responsive irreversible behavior resulting in brittleness and high yield stress. Next, we discovered a universal relationship between the mechanical properties of ink and printability that is supported by machine learning: a high elastic modulus improves shape fidelity and extrusion is possible below the critical yield stress; this is supported by machine learning. Based on this relationship, we derived various formulations of naturally derived bioinks that provide high shape fidelity using multiple regression analysis. Finally, we produced a 3D construct of a cell-laden hydrogel with a framework of high shape fidelity bioink, confirming that cells are highly viable and proliferative in the 3D constructs.