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Constraining the timescales of sediment transport by glacier systems is important for understanding the processes controlling sediment dynamics within glacierized catchments, and because the accumulation of supraglacial sediment influences glacier response to climate change. However, glacial sediment transport can be difficult to observe; sediment can be transported englacially, subglacially, supraglacially or at the ice margins, and may be stored temporarily on headwall slopes or within moraines before being (re‐)entrained and transported by glacier ice. This study is a proof of concept of the use of luminescence rock surface burial dating to establish rates of englacial sediment transport. Our novel approach combines luminescence rock surface burial dating of englacial clasts with an ice‐flow model that includes Lagrangian particle tracking to quantify rates of sediment transport through the Miage Glacier catchment in the Italian Alps. Luminescence rock surface burial ages for seven samples embedded in the near‐surface ice in the ablation area range from 0.0 ± 1.0 to 4.7 ± 0.3 ka and are consistent with the ice‐flow model results. Our results show that the transport durations of individual clasts vary by an order of magnitude, implying rapid clast transport near the glacier surface and longer transport histories for clasts transported lower in the ice column. In some cases, clasts were stored on the headwalls or within ice‐marginal moraines for several thousand years before being englacially transported. The results illustrate the different routes by which glaciers transport sediment and provide the first direct measurements of englacial sediment transport duration.