In recent years, a controversy has developed as to whether, within a few decades, renewable energies could meet all the world energy needs, without jeopardising economic growth. From the many articles that have been published, no consensus can be found regarding the answer to this question. To shed a new light on this debate, a new methodology has been developed in this thesis to estimate global wind and solar potentials and the associated Energy Return On Investment (EROI), as these two resources are expected to be the main energy sources of the future energy system. Additionally, the obtained results have been coupled with a macroeconomic model to assess the feasibility and the economic impacts of the energy transition. The estimation of the potentials includes onshore and offshore wind, solar photovoltaic and concentrated solar power plants. Based on a spatial discretisation of the world, the model calculates, per site and for each of the technologies used on the site: the production potential, the direct and indirect energy inputs required per unit of energy produced and, by relating the two previous quantities, the site EROI. The model shows that, although having a twice higher global potential, solar technologies present lower EROIs than wind technologies. The global worldwide potentials obtained lie in the lower ranges of the estimations found in the literature, while for the European countries, the total potential is equivalent to the current final energy consumption of this region. This maximum potential can only be achieved if all of the theoretically available areas are covered with wind farms and solar fields, including areas with low energy profitability, especially for solar power plants. This theoretical potential then varies significantly depending on the minimum EROI threshold that is considered sustainable. It would imply that the actually achievable potential will partly depend on the maximum price, in terms of direct and indirect energy uses, at which we can afford to produce our energy in the future. In order to take into account the interactions between the energy system and the rest of the economy, a macroeconomic model has been developed. When results of the energy model are coupled with this macroeconomic model, simulations show that in a business-as-usual context, a complete energy transition on a global scale is unachievable before the end of the century. The reason lies in the increasing capital needs of the energy sector as the share of renewable energies progresses, which slows, if not stops, economic growth and the energy transition itself. Provided that (i) future energy demand remains similar to its current level, (ii) a sufficient rate of capital growth is sustained (above its historical level), and (iii) substantial progress is made in terms of energy efficiency, a complete transition could be achieved by 2070. However, this strategy requires a significant increase in the savings rate with a negative impact on public and private consumption, which would end up stagnating at the end of the transition. The EROI decreases during the energy transition, but not significantly, suggesting that it would be the increase in the capital intensity of the energy sector that is mainly responsible for the slowdown in economic activity.