Corporate green transformation is important for the realization of China’s “double carbon” goal and the construction of a green economy, but existing studies only explored the role of policy factors or internal corporate factors in influencing them, ignoring the driving factors of corporate green transformation in an industry. Based on the perspective of inter-industry enterprise linkage, combined with principal–agent theory and signaling theory, this study uses the data of Shanghai and Shenzhen A-share listed companies from 2010 to 2021 and employs multiple linear regression to investigate the impact of common institutional ownership on corporate green transformation and its mechanism of action. The empirical findings show that common institutional ownership can significantly promote corporate green transformation, and the findings still hold after robustness tests. Principal–agent costs, total factor productivity, financing constraints, and business credit play a partial mediating role in this, and common institutional ownership has a better promotion effect on the enhancement of the degree of the green transformation of enterprises in non-heavily polluted industries. The results of this study not only can enrich the research on the economic consequences of joint institutional ownership but also have important guiding significance for China to promote the green transformation of enterprises and build a green economic system.