The 2014–2015 CE rift event associated with the Bárðarbunga eruption at Holuhraun, Iceland, offers a unique opportunity to study the spatial and temporal evolution of a rift graben. We present the first four-dimensional (three-dimensional plus time) monitoring of the formation and evolution of a graben during active magma transport using a suite of digital elevation models spanning from shortly before the eruption throughout 6 months of magma transport and up to 4.5 years after the eruption. This multiscale data set enables investigations of how magma supply and eruption dynamics affect tectonic structures that feed eruptions. After formation (time scale of a few days), the graben is remarkably stable throughout the eruption and for years beyond. It is unaffected by large changes in eruptive activity and effusion and seismicity rates within the plumbing system. These data document that (1) there was no direct feedback between eruptive dynamics and graben topography, and (2) graben formation is near instantaneous on tectonic time scales. These results challenge the overarching role ascribed to magma transport in recent studies of tectonomagmatic relationships in rift events, favoring regional tectonics as the fundamental driving force.