Unmet medical needs in treating critical-size bone defects have led to the development of numerous innovative bone tissue engineering implants. Although additive manufacturing allows flexible patient-specific treatments by modifying topological properties with various materials, the development of ideal bone implants that aid new tissue regeneration and reduce post-implantation bone disorders has been limited. Natural biomolecules are gaining the attention of the health industry due to their excellent safety profiles, providing equivalent or superior performances when compared to more expensive growth factors and synthetic drugs. Supplementing additive manufacturing with natural biomolecules enables the design of novel multifunctional bone implants that provide controlled biochemical delivery for bone tissue engineering applications. Controlled release of naturally derived biomolecules from a three-dimensional (3D) printed implant may improve implant-host tissue integration, new bone formation, bone healing, and blood vessel growth. The present review introduces us to the current progress and limitations of 3D printed bone implants with drug delivery capabilities, followed by an in-depth discussion on cutting-edge technologies for incorporating natural medicinal compounds embedded within the 3D printed scaffolds or on implant surfaces, highlighting their applications in several pre- and post-implantation bone-related disorders.