Volcanic activity at convergent plate margins is localized along lineaments of active volcanoes that focus rising magma generated within the mantle below. In many arcs worldwide, particularly continental arcs, the volcanic front migrates away from the interface of subduction (the trench) over millions of years, reflecting co-evolving surface forcing, tectonics, crustal magma transport and mantle flow. Here we show that extraction of melt from arc mantle and subsequent magmatic thickening of overlying crust and lithosphere can drive volcanic front migration. This processes is consistent with geochemical trends, such as increasing La/Yb, which show that increasing depths of differentiation correlate with arc front migration in continental arcs. Such thickening truncates the underlying mantle flow field, squeezing hot mantle wedge and the melting focus away from the trench while progressively decreasing the volume of melt generated. However, if magmatic thickening is balanced by tectonic extension in the upper plate, a steady crustal thickness is achieved that results in a more stationary arc front with long-lived mantle melting. This appears to be the case for some island arcs. Thus, in combination with tectonic modulation of crustal thickness, magmatic thickening provides a self-consistent model for volcanic arc front migration and the composition of arc magmas.