The origin of the Mediterranean Outflow is investigated by deploying six millions virtual Lagrangian parcels at the Strait of Gibraltar, and tracing them backward in time using velocity estimates from an eddy-permitting reanalysis. The Lagrangian parcels are followed until they intercept one of three sections. The hypothesis is that each section is associated with distinct water masses: the Gulf of Lions, related to Western Mediterranean Deep Water and Western Intermediate Water, carries 86% of the Outflow's transport; the Northern Tyrrhenian, related to Tyrrhenian Deep and Intermediate Waters, carries 1% of the transport; the Strait of Sicily, related to Levantine Intermediate Waters, carries 13% of the transport. The median transit times from the sections to the Strait of Gibraltar range from 5 years (Gulf of Lions) to 8 years (Strait of Sicily).