The circular economy is promoted as a contributor to sustainable development; however, the process of circular business model innovation remains under‐explored to date, hindering its implementation. Dynamic capabilities research provides a theoretical perspective to explore how incumbent firms can innovate in rapidly changing environments. An abductive qualitative research is done through an exploratory multiple case study on 10 incumbents that implemented a circular business model innovation. We identify 26 practices, aggregated in 12 micro‐foundations of the dynamic capabilities of sensing, seizing, and reconfiguring. By integrating the few empirical studies characterizing dynamic capabilities for sustainability‐oriented business model innovation, we offer a comprehensive framework of 33 practices. This study proposes that the most relevant practices for circular business model innovation processes are adopting a lifecycle perspective, employing sustainability‐oriented instruments, ideating sustainable value propositions, developing a sustainability strategy and culture, and engaging and coordinating stakeholders in the business ecosystem. We also suggest seven particularly relevant practices for long‐term business model transformations (e.g., top management commitment), four for innovations focused on short and medium loops of the circular economy (e.g., early customer engagement), and four for long loops (e.g., business ecosystem coordination). This study corroborates and expands recent research on dynamic capabilities for sustainability‐oriented innovation and provides practitioners with a set of 33 skills, processes, procedures, and activities to be prioritized to successfully innovate their business models for the circular economy.