Large-volume caldera-forming eruptions of silicic magmas are an important feature of continental volcanism. The timescales and mechanisms of assembly of the magma reservoirs that feed such eruptions as well as the durations and physical conditions of upper-crustal storage remain highly debated topics in volcanology. Here we explore a comprehensive data set of isotopic (O, Hf) and chemical proxies in precisely U-Pb dated zircon crystals from all caldera-forming eruptions of Yellowstone supervolcano. Analysed zircons record rapid assembly of multiple magma reservoirs by repeated injections of isotopically heterogeneous magma batches and short pre-eruption storage times of 103 to 104 years. Decoupled oxygen-hafnium isotope systematics suggest a complex source for these magmas involving variable amounts of differentiated mantle-derived melt, Archean crust and hydrothermally altered shallow-crustal rocks. These data demonstrate that complex magma reservoirs with multiple sub-chambers are a common feature of rift- and hotspot related supervolcanoes. The short duration of reservoir assembly documents rapid crustal remelting and two to three orders of magnitude higher magma production rates beneath Yellowstone compared to continental arc volcanoes. The short pre-eruption storage times further suggest that the detection of voluminous reservoirs of eruptible magma beneath active supervolcanoes may only be possible prior to an impending eruption.