In the past 20 years, recycled aggregate concrete (RAC), as a type of low-carbon concrete, has become a worldwide focus of research. However, the design methodology for RAC structural components remains a challenge. Consequently, demands for a unified design of natural aggregate concrete (NAC) and RAC components have been presented. Accordingly, this study analyses the necessity of a unified design theory and provides an in-depth demonstration of the strength determination, compressive constitutive relationship, and design method of concrete components. The coefficient of variation of RAC strength is found to be generally higher than that of NAC strength. The compressive and tensile strengths of RAC can be defined and determined using the same method as that used for NAC. The uniaxial compressive constitutive relationship between NAC and RAC has a unified mathematical expression. However, the elastic modulus of RAC decreases, and its brittleness exhibits an increasing trend compared with that of NAC. Finally, to unify the design formulae of RAC and NAC components for bearing capacity, modification factors for RAC components are proposed considering safety and reliability. Additionally, the feasibility of the proposed unified time-dependent design theory is demonstrated in terms of conceptual design and structural measures considering the effects of strength degradation and reinforcement corrosion. It is believed that this study enriches and develops the basic theory of concrete structures.