Rapid technological innovations are changing the jobs that Science, Technology, Engineering, and Mathematics (STEM) students are employed in after completing their education. Therefore, employers are looking for applicants with skills beyond the specialised professional competencies that can be acquired in the chosen subjects during formal education. Higher education institutions (HEIs) have an important role to play in this process, as they endeavour to equip graduates with the skills and knowledge for future jobs. Our study aims to identify the key competencies that Slovenian and Norwegian companies expect from graduates of selected STEM degree programmes in both countries. Based on these findings, the participating HEIs can tailor their degree programmes to the employability requirements of companies. This study first analysed European and international recommendations and initiatives relevant to skills development in STEM employment and education. We selected 30 key competencies and included them in the questionnaires in which companies’ human resources managers (HRMs) defined their attitudes towards employability skills in the future. We focused on companies employing graduates of the Ecotechnologies and Civil and Environmental Engineering programmes of the participating HEIs. The analysis of the results showed that companies in the two countries have different attitudes towards skills. Four competencies were identified as more important in both countries: (i) management and design of processes, technologies, and people’s work, (ii) adaptation to changes, (iii) ability to manage uncertainty, and (iv) innovation. Based on the analysis, we have developed a framework of ten employability skills for STEM students. In addition, this study provides the basis for operating a decision support system (DSS) to monitor the development of students’ competencies. The DSS is being developed as part of the RESPO-VI project supported by the Norway Grants to better match the skills of STEM students as future job seekers with the needs of potential employers. The study’s results will also help other formal and non-formal education adapt their curricula and thus reduce the employability skill gaps between current STEM education and future labour market needs.