Abstract Future dynamics of biological invasions are highly uncertain because they depend on multiple environmental, societal and socio-economic drivers. We adopted a qualitative scenario approach to explore the future of invasive alien species (IAS) in Europe and created an overall strategy for their management that considers different plausible future developments. The scenarios and strategy were developed during two online workshops with a multidisciplinary team of experts. First, we downscaled four global scenarios of biological invasions to the European level. Second, we developed a management strategy structured into 19 goals that cover a broad array of IAS-related topics (i.e. policy, research, public awareness and biosecurity), and provided solutions for achieving these goals considering the European scenarios. Third, we identified four interrelated recommendations around which any long-term strategy for managing IAS in Europe can be structured: (i) a European biosecurity regime, (ii) a dedicated communication strategy, (iii) data standardization and management tools, and (iv) a monitoring and assessment system. Finally, we identified the feasibility of the IAS management strategy, finding strong differences among the four scenarios. High levels of technological development, public environmental awareness, and effectiveness of IAS policies facilitated the implementation of the overall management strategy. Together, our results indicate that it is time for a new management of biological invasions in Europe based on a more integrative perspective across sectors and countries to be better prepared for future challenges.