Continental-scale rivers with a sandy bed sequester a significant proportion of their sediment load in flood plains. The spatial extent and depths of such deposits have been described, and flood-plain accumulation has been determined at decadal timescales, but it has not been possible to identify discrete events or to resolve deposition on near-annual timescales. Here we analyse (210)Pb activity profiles from sediment cores taken in the pristine Beni and Mamore river basins, which together comprise 720,000 km2 of the Amazon basin, to investigate sediment accumulation patterns in the Andean-Amazonian foreland. We find that in most locations, sediment stratigraphy is dominated by discrete packages of sediments of uniform age, which are typically 20-80 cm thick, with system-wide recurrence intervals of about 8 yr, indicating relatively rare episodic deposition events. Ocean temperature and stream flow records link these episodic events to rapidly rising floods associated with La Niña events, which debouch extraordinary volumes of sediments from the Andes. We conclude that transient processes driven by the El Niño/Southern Oscillation cycle control the formation of the Bolivian flood plains and modulate downstream delivery of sediments as well as associated carbon, nutrients and pollutants to the Amazon main stem.