Many researchers and practitioners agree that a specific skillset helps to provide good healthcare to migrant and minority patients. The sciences offer multiple terms for what we are calling ‘diversity competence’. We assume that teaching and developing this competence is a complex, time-consuming task, yet health professionals’ time for further training is limited. Consequently, teaching objectives must be prioritised when creating a short, basic course to foster professionals’ diversity competence. Therefore, we ask: ‘What knowledge, attitudes and skills are most important to enable health professionals to take equally good care of all patients in evermore diverse, modern societies that include migrant and (ethnic) minority patients?’ By means of a modified, two-round Delphi study, 31 clinical and academic migrant health experts from 13 European countries were asked this question. The expert panel reached consensus on many competences, especially regarding attitudes and practical skills. We can provide a competence ranking that will inform teaching initiatives. Furthermore, we have derived a working definition of ‘diversity competence of health professionals’, and discuss the advantages of the informed and conscious use of a ‘diversity’ instead of ‘intercultural’ terminology