El Niño/La Niña, characterized by anomalous sea surface temperature warming/cooling in the central-eastern equatorial Pacific, is a dominant interannual variability with irregularity, impacting worldwide weather and socioeconomics. The observed records show that La Niña often persists for more than two years, called “multi-year La Niña” which tends to accompany extreme El Niño in the preceding year; however, the physical linkage between them remains unclear. Here we show using reanalysis data that an extreme El Niño excites atmospheric conditions that favor the generation of the multi-year La Niña in subsequent years. Easterly wind anomalies along the northern off-equator in the Pacific during the decay phase of an extreme El Niño are crucial. They act to discharge ocean heat content (OHC) via an anomalous northward Ekman transport; the negative OHC anomaly is large enough to be restored by a single La Niña and, therefore, causes another La Niña to occur in the second year. Furthermore, analyses of the Coupled Model Intercomparison Project Phase 6 (CMIP6) models show that the occurrence frequencies of multi-year La Niña and extreme El Niño are highly correlated, supporting the abovementioned mechanism. Our results provide physical evidence that the increasing frequency of multi-year La Niña is explained by the increasing El Niño amplitude since the late 20th century.