The present study investigates the rebound hammer number (RHN), ultrasonic pulse velocity (UPV), compressive strength, split tensile strength, and modulus of elasticity of concrete made with recycled coarse aggregate and bottom ash. The natural coarse aggregates (crushed rock aggregates) and fine aggregates (sand) are partially or fully replaced (0%, 50%, and 100%) with recycled coarse aggregates (RCA) and coal bottom ash (BA), respectively. Standard concrete specimens were then cast to determine the former properties at 28- and 90-days of curing. The experimentally obtained RCA and BA concrete properties are found comparable to conventional concrete. It has been observed that 100% RCA concrete properties at 90 days are similar to the 28 days of conventional concrete properties. Scanning electron microscope (SEM) analysis has also been performed to examine the mechanism behind the observed properties of RCA, BA, and RCA + BA (concrete containing both RCA and BA) concrete. Based on the experimentally obtained 28-day compressive strength, UPV, and RHN values, the analytical models for predicting the compressive strength, splitting tensile strength, and static modulus of elasticity of RCA, BA, and RCA + BA concrete at any age are also proposed. The values calculated from the proposed models are in good agreement with the experiments. The present study will be helpful for the designers and engineers in practice for fixing preliminary dimensions of concrete elements made with RCA, BA, and RCA + BA concrete mixes, thus leading to sustainable concrete construction.