An environmentally sustainable and thus green business process is one that delivers organizational value whilst also exerting a minimal impact on the natural environment. Recent works from the field of Information Systems (IS) have argued that information systems can contribute to the design and implementation of sustainable busi-ness processes. While prior research has investigated how information systems can be used in order to support sustainable business practices, there is still a void as to the actual changes that business processes have to undergo in order to become environmentally sustainable, and the specific role that information systems play in enabling this change. In this paper, we provide a conceptualization of environmentally sustainable business processes, and discuss the role of functional affordances of information systems in enabling both incremental and radical changes in order to make processes environmentally sustainable. Our conceptualization is based on (a) a fundamental definition of the concept of environmental sustainability, grounded in two basic components: the environmental source and sink functions of any project or activity, and (b) the concept of functional af-fordances, which describe the potential uses originating in the material properties of information systems in relation to their use context. In order to illustrate the application of our framework and provide a first evalua-tion, we analyse two examples from prior research where information systems impacted on the sustainability of business processes.