At geologic timescales, many proxy data suggest a contrasting evolution of Asian and African monsoons since the Oligocene. The Asian summer monsoon increases drastically around 8 Ma, whereas the African summer monsoon gradually weakens during the Miocene. Using an atmospheric general circulation model, we simulate most of the spatial evolutions of both monsoons only accounting for the changes of paleogeography, including continental drift, orogeny, and sea level change. The paleogeographic changes modify drastically the climate over central and southern Asia between the Oligocene and the present. The retreat of an epicontinental sea warms central Eurasia in summer. The heating of this area and the uplifts of the Tibetan plateau and of the Himalayas deepen the Asian low-pressure cell and displace it northwest. This then shifts precipitation from Indochina toward the southern flank of the Himalayas. This is in good agreement with proxy data. Therefore our modeling studies support a shift and a strengthening of the Asian monsoon during the late Tertiary rather than a real "onset". We suggest that the increase in seasonal precipitation and the strengthening of the number of days with heavy rainfall over the Himalayas from 30 Ma to the present may be of critical importance to explain the long-term evolution of physical erosion of this area. We also investigate the respective impact of the Paratethys shrinkage and of the Tibetan plateau uplift through sensitivity experiments and prove that the Paratethys retreat plays an important role in monsoon evolution. The northward drift of the African continent confines summer monsoon precipitation to a thin belt which favors the stretching of the subtropical desert, in good agreement with data. We finally show that during the Oligocene, the African and Asian monsoon systems are clearly separated by the Tethys seaway. The closure of this seaway and the evolution of the Asian monsoon induce a connection between both monsoon systems in the low and middle troposphere.