A solid foundation for all people to share the developmental achievements of the digital era is established by computing infrastructure, which serves as a critical support for the solid advancement of common prosperity. Panel data of 254 prefecture-level and above cities in China from 2012 to 2024 were adopted for research. Evaluation index systems for computing infrastructure and common prosperity were constructed, and the entropy weight method is applied for quantitative measurement. The impact effect and mechanism of computing infrastructure construction on common prosperity were systematically analyzed. Empirical results demonstrate that common prosperity is significantly and positively promoted by the construction of computing infrastructure. Mediating effect tests verify that computing infrastructure construction facilitates common prosperity through three effective channels, including industrial structure upgrading, employment structure optimization, and consumption expansion and quality improvement. Heterogeneity tests confirm that the empowering effect of computing infrastructure construction on common prosperity presents obvious urban differentiation characteristics. The effect is stronger in cities with high administrative levels than in ordinary cities and stronger in cities with high-level intellectual property protection than in cities with low-level intellectual property protection. The influence of computing infrastructure construction on common prosperity also shows a hierarchical characteristic of the common prosperity dimension > sharing dimension > sustainability dimension. Threshold effect tests indicate that the promotion effect of computing infrastructure construction on common prosperity is constrained by a double threshold of talent digital literacy and a single threshold of market-oriented allocation of data elements. Targeted suggestions are proposed to accelerate the construction of an inclusive mechanism for computing power services and smooth the empowerment path of digital infrastructure. Relevant research conclusions provide effective references for promoting substantive progress in common prosperity.