In recent years, the European Union has advanced towards responsible and sustainable Artificial Intelligence (AI) research, development and innovation. While the Ethics Guidelines for Trustworthy AI released in 2019 and the AI Act in 2021 set the starting point for a European Ethical AI, there are still several challenges to translate such advances into the public debate, education and practical learning. This paper contributes towards closing this gap by reviewing the approaches that can be found in the existing literature and by interviewing 11 experts across five countries to help define educational strategies, competencies and resources needed for the successful implementation of Trustworthy AI in Higher Education (HE) and to reach students from all disciplines. The findings are presented in the form of recommendations both for educators and policy incentives, translating the guidelines into HE teaching and practice, so that the next generation of young people can contribute to an ethical, safe and cutting-edge AI made in Europe.