Interdecadal changes in the potential predictability of the East Asian summer monsoon (EASM) and South Asian summer monsoon (SASM) were investigated using the signal‐to‐noise ratio of daily reanalysis data from 1948 to 2017. Results reveal that variations in the SASM predictability are out of phase with those in EASM predictability, and that SASM predictability is higher (lower) than EASM predictability before (after) the 1980s. The out‐of‐phase relationship of the predictability of the two monsoon systems is attributed mainly to temporal changes in their relationships with El Niño‐Southern Oscillation (ENSO). The relationship between the EASM and ENSO is related to the position of the ENSO heating center, which is located in the central Pacific before the 1980s but shifted to the eastern Pacific after the 1980s, accompanied by a strengthening (weakening) in the relationship between ENSO and the EASM (SASM). The shift in the position of the ENSO heating center was found to have contributions from the modulation of the Pacific decadal oscillation.