Many studies point to a robust ENSO signature on the North Atlantic–European (NAE) sector associated with a downstream effect of Rossby wave trains. Some of these works also address a nonstationary behavior of the aforementioned link, but only few have explored the possible modulating factors. In this study the internal causes within the ocean–atmosphere coupled system influencing the tropospheric ENSO–Euro-Mediterranean rainfall teleconnection have been analyzed. To this aim, unforced long-term preindustrial control simulations from 18 different CMIP5 models have been used. A nonstationary impact of ENSO on Euro-Mediterranean rainfall, being spatially consistent with the observational one, is found. This variable feature is explained by a changing ENSO-related Rossby wave propagation from the tropical Pacific to the NAE sector, which, in turn, is modulated by multidecadal variability of the climatological jet streams associated with the underlying sea surface temperature (SST). The results, therefore, indicate a modulation of the ENSO–Euro-Mediterranean rainfall teleconnection by the internal (and multidecadal) variability of the ocean–atmosphere coupled system.