The centrosome is a major microtubule organizing center in animal cells. The position of the centrosomes inside the cell is important for cell functions such as cell cycle, and thus should be tightly regulated. Theoretical models based on the forces generated along the microtubules have been proposed to account for the dynamic movements of the centrosomes during the cell cycle. These models, however, often adopted inconsistent assumptions to explain distinct but successive movements, thus preventing a unified model for centrosome positioning. For the centration of the centrosomes, weak attachment of the astral microtubules to the cell cortex was assumed. In contrast, for the separation of the centrosomes during spindle elongation, strong attachment was assumed. Here, we mathematically analyzed these processes at steady state and found that the different assumptions are proper for each process. We experimentally validated our conclusion using nematode and sea urchin embryos by manipulating their shapes. Our results suggest the existence of a molecular mechanism that converts the cortical attachment from weak to strong during the transition from centrosome centration to spindle elongation.