Genomic science is increasingly central to the provision of health care. Producing and applying robust genomics knowledge is a complex endeavour in which no single individual, profession, discipline or community holds all the answers. Engagement and involvement of diverse stakeholders can support alignment of societal and scientific interests, understandings and perspectives and promises better science and fairer outcomes. In this context we argue for F.A.I.R.E.R. data and data use that is Findable, Accessible, Interoperable, Reproducible, Equitable and Responsible. Yet there is a paucity of international guidance on how to engage publics, patients and participants in genomics. To support meaningful and effective engagement and involvement we developed an Engagement Framework for involving and engaging participants, patients and publics in genomics research and health implementation. The Engagement Framework is intended to support all those working in genomics research, medicine, and healthcare to deliberatively consider approaches to participant, patient and public engagement and involvement in their work. Through a series of questions, the Engagement Framework prompts new ways of thinking about the aims and purposes of engagement, and support reflection on the strengths, limitations, likely outcomes and impacts of choosing different approaches to engagement. To guide genomics activities, we describe four themes and associated questions for deliberative reflection: (i) fairness; (ii) context; (iii) heterogeneity, and (iv) recognising tensions and conflict. The four key components in the Engagement provide a framework to assist those involved in genomics to reflect on decisions they make for their initiatives, including the strategies selected, the participant, patient and public stakeholders engaged, and the anticipated goals. The Engagement Framework is one step in an actively evolving process of building genomics research and implementation cultures which foster responsible leadership and are attentive to objectives which increase equality, diversity and inclusion in participation and outcomes.