A central problem in the study of human mobility is that of migration systems. Typically, migration systems are defined as a set of relatively stable movements of people between two or more locations over time. While these emergent systems are expected to vary over time, they ideally contain a stable underlying structure that could be discovered empirically. There have been some notable attempts to formally or informally define migration systems, however they have been limited by being hard to operationalize, and by defining migration systems in ways that ignore origin/destination aspects and/or fail to account for migration dynamics. In this work we propose a novel method, spatio-temporal (ST) tensor co-clustering, stemming from signal processing and machine learning theory. To demonstrate its effectiveness for describing stable migration systems we focus on domestic migration between counties in the US from 1990-2018. Relevant data for this period has been made available through the US Internal Revenue Service. Specifically, we concentrate on three illustrative case studies: (i) US Metropolitan Areas, (ii) the state of California, and (iii) Louisiana, focusing on detecting exogenous events such as Hurricane Katrina in 2005. Finally, we conclude with discussion and limitations of this approach.