The global transport sector is one of the main sources of anthropogenic greenhouse gas emissions representing one quarter of all energy related greenhouse gas emissions. Defossilisation of the transport is an important part of the transition towards a carbon-neutral energy system. Fast development of electric mobility technologies, fast growth of renewable electricity generation and emerging power-to-fuels sector provide the means for such a transition. The transition simulation presented in this study focuses on the transport sector using an energy system model in hourly resolution and the transition reaches 100% renewable energy supply by 2050. Results show that massive electrification emerges as the main path for the transport sector, while in some segments, where direct electrification is not possible, demand is satisfied with renewable electricity-based fuels. In every region of the world, the existing renewable energy potential is more than sufficient to satisfy the transport sector demand even with fast growth. The transition leads to significant improvement in energy efficiency both on the demand side, due to more efficient engines and electric motors, and the supply side, with the switch to renewable electricity supply. Solar photovoltaics evolve to become the main source of energy for the transport sector by mid-century.