Delirium is common in hospitalised patients, and there is currently no specific treatment. Identifying and treating underlying somatic causes of delirium is the first priority once delirium is diagnosed. Several international guidelines provide clinicians with an evidence-based approach to screening, diagnosis and symptomatic treatment. However, current guidelines do not offer a structured approach to identification of underlying causes. A panel of 37 internationally recognised delirium experts from diverse medical backgrounds worked together in a modified Delphi approach via an online platform. Consensus was reached after five voting rounds. The final product of this project is a set of three delirium management algorithms (the Delirium Delphi Algorithms), one for ward patients, one for patients after cardiac surgery and one for patients in the intensive care unit.