This study employed the wavelet empirical orthogonal function (WEOF) analysis to analyse the nonstationary variability of rainfall in Ethiopia and global sea surface temperature (SST) for 1900–1998. The study found that the nonstationary variations of both the June to September (JJAS) and February to May (FMAM) Ethiopian rainfall can be delineated into three zones: western half of Ethiopia north of the Great Rift Valley (GRV), southern Ethiopia south of the GRV and the GRV from southwestern Ethiopia to the Afar Triangle. The leading wavelet principal component (WPC) signals showed that Ethiopian rainfall had been in stagnation for most of 1900–1998, with major droughts in the 1940s and 1980s. The dominant frequencies of Ethiopian rainfall ranged between 2 and 8 years. In western Ethiopia, the 2–4-year rainfall frequencies dominated the rainfall variation, but their trends are modulated by 5–7-year frequencies, whereas in the Afar Triangle, the 5–7-year frequencies were dominant. Between 1900 and 1998, the Afar Triangle region experienced decreasing rainfall for 60 years (1900–1960). The seasonal global SST revealed that regardless of what time of the year, the strongest contributions to global SST variations occur in the Antarctic Ocean, the El Niño region of South America and in the southwestern Pacific Ocean, followed by the Atlantic and the Indian Oceans. Further, this study also shows annual migrations of SST variations in the El Niño region, the Antarctic and the Atlantic Oceans. The leading SST signal variations show that SST warming started in the Atlantic and Indian Oceans, from 1950 to 1975, and spread to the Antarctic Ocean between 1960 and 1990, which probably contributed to the melting of sea ice. Teleconnections between WPC1 of Ethiopian rainfall and SST scale-averaged wavelet power were found for the El Niño region and northern Atlantic, west of the Sahara desert.