The use of digital technology is increasing rapidly across surgical specialities, yet there is no consensus for the term 'digital surgery'. This is critical as digital health technologies present technical, governance, and legal challenges which are unique to the surgeon and surgical patient. We aim to define the term digital surgery and the ethical issues surrounding its clinical application, and to identify barriers and research goals for future practice. 38 international experts, across the fields of surgery, AI, industry, law, ethics and policy, participated in a four-round Delphi exercise. Issues were generated by an expert panel and public panel through a scoping questionnaire around key themes identified from the literature and voted upon in two subsequent questionnaire rounds. Consensus was defined if >70% of the panel deemed the statement important and <30% unimportant. A final online meeting was held to discuss consensus statements. The definition of digital surgery as the use of technology for the enhancement of preoperative planning, surgical performance, therapeutic support, or training, to improve outcomes and reduce harm achieved 100% consensus agreement. We highlight key ethical issues concerning data, privacy, confidentiality and public trust, consent, law, litigation and liability, and commercial partnerships within digital surgery and identify barriers and research goals for future practice. Developers and users of digital surgery must not only have an awareness of the ethical issues surrounding digital applications in healthcare, but also the ethical considerations unique to digital surgery. Future research into these issues must involve all digital surgery stakeholders including patients.