Despite substantial attention given to the development of osteoregenerative biomaterials, severe deficiencies remain in current products. These limitations include an inability to adequately, rapidly, and reproducibly regenerate new bone; high costs and limited manufacturing capacity; and lack of surgical ease of handling. To address these shortcomings, we generated a new, synthetic osteoregenerative biomaterial, hyperelastic “bone” (HB). HB, which is composed of 90 weight % (wt %) hydroxyapatite and 10 wt % polycaprolactone or poly(lactic-co-glycolic acid), could be rapidly three-dimensionally (3D) printed (up to 275 cm3/hour) from room temperature extruded liquid inks. The resulting 3D-printed HB exhibited elastic mechanical properties (~32 to 67% strain to failure, ~4 to 11 MPa elastic modulus), was highly absorbent (50% material porosity), supported cell viability and proliferation, and induced osteogenic differentiation of bone marrow–derived human mesenchymal stem cells cultured in vitro over 4 weeks without any osteo-inducing factors in the medium. We evaluated HB in vivo in a mouse subcutaneous implant model for material biocompatibility (7 and 35 days), in a rat posterolateral spinal fusion model for new bone formation (8 weeks), and in a large, non-human primate calvarial defect case study (4 weeks). HB did not elicit a negative immune response, became vascularized, quickly integrated with surrounding tissues, and rapidly ossified and supported new bone growth without the need for added biological factors.