The core element of climate change is the sensitivity of the Earth's climate system to the balance between incoming solar radiation and outgoing terrestrial radiation at the top of the atmosphere. CO2 is one of the key atmospheric parameters controlling the outgoing longwave radiation. In this paper, hyper-spectral satellite data of the outgoing long wave radiation from a decade of observations are successfully used for the first time to disentangle the radiative effect of CO2 increase from those of other relevant parameters such as temperature and water vapour variations. The paper demonstrates convincingly that the observed radiative changes agree excellently with theoretical predictions of outgoing long wave radiation changes due to the observed CO2 increase. While solely based on observations from space, these results confirm a fundamental theoretical underpinning of the science of global warming.