Here we present an MRI-based approach to assess breast cancer related lymphoedema tissue composition (fluid, fat, and muscle volumes) and we evaluate a cohort of 13 patients. Our measurements indicate that fat, which cannot be eliminated by first line treatment, was the predominant component of the swelling. Furthermore, changes in tissue composition were not uniform along the arm. Quantification of the volume and spatial distribution of different tissue components could greatly improve treatment delivery and patient selection for optimal treatment. With a 6 minute MRI scan and automated post-processing, this methodology shows potential for implementation in clinical practice.