Continental rifting, the break-up of continents to form ocean basins, is a key component in the tectonic cycle affecting Earth’s surface environment. The early rifting process involves extension via the movement of large faults, but late-stage rifts are characterised by magmatic activity, which weakens the crust by heating it. Constraining how and when these magmatic systems develop is important for understanding how continental rifts develop into mid-ocean ridges. Here we consider the Main Ethiopian Rift, a rift zone intermediate between early- and late-stage continental rifting. We study olivine crystals from Main Ethiopian Rift volcanoes that have compositional zones—layers of differing compositions that reflect the changing compositions of the magmas they grow from. Our samples, from two different parts of the rift, have similar zoning patterns, suggesting that common processes operate in rift volcanic systems. By simulating the diffusion of elements between these olivine compositional zones, we determine that Ethiopian Rift magmas consistently take weeks to months to move through the crust. This is a similar timescale to magma movement recorded by geophysical methods at late-stage rift zones in Iceland and Afar, and demonstrates that the magmatic structure of these late-stage rifts is already present in Ethiopia despite its comparative immaturity.