Climate change may cause most harm to countries that have historically contributed the least to greenhouse gas emissions and land-use change. This paper identifies consequentialist and non-consequentialist ethical principles to guide a fair international burden-sharing scheme of climate change adaptation costs. We use these ethical principles to derive political principles - historical responsibility and capacity to pay - that can be applied in assigning a share of the financial burden to individual countries. We then propose a hybrid 'common but differentiated responsibilities and respective capabilities' approach as a promising starting point for international negotiations on the design of burden-sharing schemes. A numerical assessment of seven scenarios shows that the countries of Annex I of the United Nations Framework Convention on Climate Change would bear the bulk of the costs of adaptation, but contributions differ substantially subject to the choice of a capacity to pay indicator. The contributions are less sensitive to choices related to responsibility calculations, apart from those associated with land-use-related emissions. Assuming costs of climate adaptation of USD 100 billion per year, the total financial contribution by the Annex I countries would be in the range of USD 65-70 billion per year. Expressed as a per capita basis, this gives a range of USD 43-82 per capita per year.