We applied a dynamic global vegetation model (DGVM) to the African continent. After calibration, the model reproduced geographical distributions of the continent's biomes, annual gross primary productivity (GPP), and biomass under current climatic conditions. The model is driven by the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emission Scenarios (SRES) A1B scenario of rising CO2, and by climate changes during the twenty‐first century resulting from the change in CO2concentrations, simulated by a coupled Model for Interdisciplinary Research on Climate (MIROC) ocean atmosphere model. Simulations under this condition revealed time lags between environmental change and biome change, with the extent of these lags depending largely on the type of biome change. A switch in forest type was accompanied by the longest delay in biome change among all changes classified, indicating that resident trees largely prevent the establishment of nonresident tree types adapted to the new environment, and that tree growth requires additional years after successful establishment. In addition, assumptions for tree dispersal, which determine whether nonresident tree types can be established, modified the patterns of biome change under the twenty‐first‐century environment: under the assumption that nonresident tree types cannot be established even if environmental conditions change, the extent of the forest type switch and the development of forest and savanna were suppressed, while forest dieback was enhanced. These changes accompanied a slowing of the increasing trend in net primary productivity (NPP), biomass, and soil carbon during the twenty‐first century and in subsequent years. These results quantitatively demonstrate that both patch dynamics and invasive tree recruitment significantly modify the transient change in vegetation distribution and function under a changing environment on the African continent.