Accessible design enables participation in the digital society for everyone. However, cognitive accessibility is not well established within the field of web design. The International Classification of Functioning, Disability and Health (ICF) provides a descriptive framework that relates health conditions to functioning and participation. ICF Core Sets are purposefully tailored shortlists of ICF categories for describing functioning. The aim of this study was to develop an ICF core set for cognitive web accessibility to be used by web designers. ICF categories with relevance for cognitive accessibility were extracted and linked to the guidelines in the standard for cognitive accessibility: ISO 21801-1, followed by interpretation of the meaning of the ICF categories in relation to cognitive accessibility. The latter was outlined as practical advice for designers on design considerations for cognitive accessibility. The analysis was performed by an iterative back-and-forth process between the lived experiences of persons with cognitive impairments, the ISO-standard and the ICF. The ICF core set comprises 46 ICF categories with design considerations for cognitive accessibility. The ICF core set is suggested to facilitate understanding of the challenges in digital design that users experience and provide strategies to address cognitive accessibility, and thereby improve design outcomes.