We study the response of the land biosphere to climate change by coupling a climate general circulation model to a global carbon cycle model. This coupled model was forced by observed CO2 emissions for the 1860--1990 period and by the IPCC SRES-A2 emission scenario for the 1991--2100 period. During the historical period, our simulated Net Primary Production (NPP) and net land uptake (NEP) are comparable to the observations in term of trend and variability. By the end of the 21st century, we show that the global NEP is reduced by 56% due to the climate change. In the tropics, increasing temperature, through an increase of evapotranspiration, acts to reduce the soil water content, which leads to a 80% reduction of net land CO2 uptake. As a consequence, tropical carbon storage saturates by the end of the simulation, some regions becoming sources of CO2. On the contrary, in northern high latitudes, increasing temperature stimulates the land biosphere by lengthening the growing season by about 18 days by 2100 which in turn leads to a NEP increase of 11%. Overall, the negative climate impact in the tropics is much larger than the positive impact simulated in the extratropics, therefore, climate change reduce the global land carbon uptake. This constitutes a positive feedback in the climate-carbon cycle system.