The Harappan Culture, one of the oldest known urban civilizations, thrived on the northwest edge of the Thar Desert (India and Pakistan) between 3200 and 1900 BCE. Its demise has been linked to rapid weakening of the summer monsoon at this time, yet reorganization of rivers may also have played a role. We sampled subsurface channel sand bodies predating ca. 4.0 ka and used U-Pb dating of zircon sand grains to constrain their provenance through comparison with the established character of modern river sands. Samples from close to archaeological sites to the north of the desert show little affinity with the Ghaggar-Hakra, the presumed source of the channels. Instead, we see at least two groups of sediments, showing similarities both to the Beas River in the west and to the Yamuna and Sutlej Rivers in the east. The channels were active until after 4.5 ka and were covered by dunes before 1.4 ka, although loss of the Yamuna from the Indus likely occurred as early as 49 ka and no later than 10 ka. Capture of the Yamuna to the east and the Sutlej to the north rerouted water away from the area of the Harappan centers, but this change significantly predated their final collapse.