This research focuses on the bonding between calcium phosphate cement (CPC) composites designed as a thin repair overlay material and old ordinary portland cement (OPC) as a concrete substrate. The OPC concrete substrate was prepared to have a 28-day compressive strength of 50 MPa at room temperature. In order to select a suitable surface condition of the substrate to receive the repair material and the age to determine the bond strength, the development of the bond strength of the CPC overlay cast on five different preconditioned old concrete substrates was measured after 7, 14, and 28 days under laboratory conditions. It was found that the prepared saturated surface dry (SSD) substrate surface had the optimum bond strengths with the CPC material after 14 days. Subsequently, the intimate bonding relationships between the in situ cast CPC composites and the precast concrete (conditioned as the prepared SSD substrate surface) were investigated through pull-off, slant shear, and bi-shear bond tests. Results indicate a high bond between the CPC repair material and the OPC concrete substrate at room temperature. It was also found that rubber aggregates and fiber inclusions reduced such bond, with the most significant detrimental effect in composites that contained rubber aggregates and fiber reinforcements. Finally, a high positive correlation was observed among the tensile bond strength, slant shear bond strength, and bi-shear bond strength of the CPC-OPC composite systems, with cohesion and coefficient of friction values ranging from 1.37–2.94 MPa and 0.78–1.07, respectively.