SummaryThe Earth’s mean surface temperature is already approximately 1.1°C higher than pre‐industrial levels. Exceeding a mean 1.5°C rise by 2050 will make global adaptation to the consequences of climate change less possible. To protect public health, anaesthesia providers need to reduce the contribution their practice makes to global warming. We convened a Working Group of 45 anaesthesia providers with a recognised interest in sustainability, and used a three‐stage modified Delphi consensus process to agree on principles of environmentally sustainable anaesthesia that are achievable worldwide. The Working Group agreed on the following three important underlying statements: patient safety should not be compromised by sustainable anaesthetic practices; high‐, middle‐ and low‐income countries should support each other appropriately in delivering sustainable healthcare (including anaesthesia); and healthcare systems should be mandated to reduce their contribution to global warming. We set out seven fundamental principles to guide anaesthesia providers in the move to environmentally sustainable practice, including: choice of medications and equipment; minimising waste and overuse of resources; and addressing environmental sustainability in anaesthetists’ education, research, quality improvement and local healthcare leadership activities. These changes are achievable with minimal material resource and financial investment, and should undergo re‐evaluation and updates as better evidence is published. This paper discusses each principle individually, and directs readers towards further important references.