Cell state transitions control the functional behavior of cancer cells. Epithelial-to-mesenchymal transition (EMT) confers cancer stem cell-like properties, enhanced tumorigenicity and drug resistance to tumor cells, while mesenchymal-epithelial transition (MET) reverses these phenotypes. Using high-throughput chemical library screens, retinoids are found to be potent promoters of MET that inhibit tumorigenicity in basal-like breast cancer. Cell state transitions are defined by reprogramming of lipid metabolism. Retinoids bind cognate nuclear receptors, which target lipid metabolism genes, thereby redirecting fatty acids for β-oxidation in the mesenchymal cell state towards lipid storage in the epithelial cell state. Disruptions of key metabolic enzymes mediating this flux inhibit MET. Conversely, perturbations to fatty acid oxidation (FAO) rechannel fatty acid flux and promote a more epithelial cell phenotype, blocking EMT-driven breast cancer metastasis in animal models. FAO impinges on the epigenetic control of EMT through acetyl-CoA-dependent regulation of histone acetylation on EMT genes, thus determining cell states.