Calcium phosphate cements (CPCs) are clinically effective void fillers that are capable of bridging calcified tissue defects and facilitating regeneration. However, CPCs are completely synthetic/inorganic, unlike the calcium phosphate that is found in calcified tissues, and they lack an architectural organization, controlled assembly mechanisms, and have moderate biomechanical strength, which limits their clinical effectiveness. Herein, we describe a new class of bioinspired CPCs that can glue tissues together and bond tissues to metallic and polymeric biomaterials. Surprisingly, alpha tricalcium phosphate cements that are modified with simple phosphorylated amino acid monomers of phosphoserine (PM-CPCs) bond tissues up to 40-fold stronger (2.5–4 MPa) than commercial cyanoacrylates (0.1 MPa), and 100-fold stronger than surgical fibrin glue (0.04 MPa), when cured in wet-field conditions. In addition to adhesion, phosphoserine creates other novel properties in bioceramics, including a nanoscale organic/inorganic composite microstructure, and templating of nanoscale amorphous calcium phosphate nucleation. PM-CPCs are made of the biocompatible precursors calcium, phosphate, and amino acid, and these represent the first amorphous nano-ceramic composites that are stable in liquids.