Deciphering the functional interactions of cells in tissues remains a major challenge. Here we describe DIALOGUE, a method to systematically uncover multicellular programs (MCPs)-combinations of coordinated cellular programs in different cell types that form higher-order functional units at the tissue level-from either spatial data or single-cell data obtained without spatial information. Tested on spatial datasets from the mouse hypothalamus, cerebellum, visual cortex and neocortex, DIALOGUE identified MCPs associated with animal behavior and recovered spatial properties when tested on unseen data while outperforming other methods and metrics. In spatial data from human lung cancer, DIALOGUE identified MCPs marking immune activation and tissue remodeling. Applied to single-cell RNA sequencing data across individuals or regions, DIALOGUE uncovered MCPs marking Alzheimer's disease, ulcerative colitis and resistance to cancer immunotherapy. These programs were predictive of disease outcome and predisposition in independent cohorts and included risk genes from genome-wide association studies. DIALOGUE enables the analysis of multicellular regulation in health and disease.