Elevated CO2 concentrations increase photosynthesis and, potentially, net ecosystem production (NEP), meaning a greater CO2 uptake. Climate, nutrients and ecosystem structure, however, influence the effect of increasing CO2. Here we analysed global NEP from MACC-II and Jena CarboScope atmospheric inversions and ten dynamic global vegetation models ( TRENDY), using statistical models to attribute the trends in NEP to its potential drivers: CO2, climatic variables and land-use change. We found that an increased CO2 was consistently associated with an increased NEP (1995-2014). Conversely, increased temperatures were negatively associated with NEP. Using the two atmospheric inversions and TRENDY, the estimated global sensitivities for CO2 were 6.0 +/- 0.1, 8.1 +/- 0.3 and 3.1 +/- 0.1 PgC per 100 ppm (similar to 1 degrees C increase), and -0.5 +/- 0.2, -0.9 +/- 0.4 and -1.1 +/- 0.1 PgC degrees C-1 for temperature. These results indicate a positive CO2 effect on terrestrial C sinks that is constrained by climate warming.