Immediately after their formation, the terrestrial planets experienced intense impact bombardment by comets, leftover planetesimals from primary accretion, and asteroids. This temporal interval in solar system evolution, termed late accretion, thermally and chemically modified solid planetary surfaces and may have impeded the emergence of life on the Hadean Earth. The sources and tempo of late accretion are, however, vague. Here, we present a timeline that relates variably retentive radiometric ages from asteroidal meteorites, to new dynamical models of late accretion that invokes giant planet migration. Reconciliation of the geochronological data with dynamical models shows that giant planet migration immediately leads to an intense 30 Myr influx of comets to the entire solar system. The absence of whole-sale crustal reset ages after 4450 Ma for the most resilient chronometers from Earth, Moon, Mars, Vesta and various meteorite parent bodies confines the onset of giant planet migration to no later than ca. 4480 Ma. Waning impacts from planetesimals, asteroids (and a minor cometary component) continue to strike the inner planets through a protracted monotonic decline in impactor flux; this is in agreement with predictions from crater chronology. Amended global 3-D thermal analytical bombardment models derived from our new impact mass-production functions show that persistent niches for prebiotic chemistry on the early Hadean Earth could endure late accretion for at least the last 4400 Myr.