There is a widespread agreement that the current linear economic system is unsustainable due to the physical boundaries of our planet and must be replaced by a circular one, that is, by a circular economy (CE). Previous studies have theoretically proposed that eco‐innovations (EIs), or innovations that reduce the environmental impacts of consumption and production processes, are a key element to improve the circular use of resources. However, the analysis of the drivers of such a transition to a CE through EI, particularly at the micro‐level of firms, has not received attention in the past. The aim of this paper is to cover this gap in the literature. It quantitatively analyses the role of influencing factors (drivers and barriers) in that relationship, with a focus on the company's organisational (‘soft’) factors, rooted in organisational culture and strategy. With the help of data collected through a survey of Spanish small and medium‐sized firms in the industrial sector, a regression‐based moderation analysis is carried out. Therefore, four moderation models were defined based on organisational factors derived from the previous literature (sustainability, future, stakeholder and learning/knowledge orientation in firms. The results suggest that, indeed, two of those factors (a high level of sustainability and knowledge orientation) are particularly relevant drivers in the transition to the CE through EI. Thus, if the aim of policy makers and corporate decision makers is to increase the circularity of the economy or their firms, policies and measures should be targeted at these two factors.