A fundamental goal in animal ecology is to quantify how environmental (and other) factors influence individual movement, as this is key to understanding responsiveness of populations to future change. However, quantitative interpretation of individual-based telemetry data is hampered by the complexity of, and error within, these multi-dimensional data. Here, we present an integrative hierarchical Bayesian state-space modelling approach where, for the first time, the mechanistic process model for the movement state of animals directly incorporates both environmental and other behavioural information, and observation and process model parameters are estimated within a single model. When applied to a migratory marine predator, the southern elephant seal (Mirounga leonina), we find the switch from directed to resident movement state was associated with colder water temperatures, relatively short dive bottom time and rapid descent rates. The approach presented here can have widespread utility for quantifying movement-behaviour (diving or other)-environment relationships across species and systems.