The power sector is faced with strict requirements in reducing harmful emissions and substantially increasing the level of sustainability. Renewable energy (RE) in general and solar photovoltaic (PV) in particular can offer societally beneficial solutions. The LUT energy system transition model is used to simulate a cost-optimised transition pathway towards 100% RE in the power sector by 2050. The model is based on hourly resolution for an entire year, the world structured in 145 regions, high spatial resolution of the input RE resource data, and transition steps of 5-year periods. The global average solar PV electricity generation contribution is found to be about 69% in 2050, the highest ever reported. Detailed energy transition results are presented for representative countries in the world, namely, Poland, Britain and Ireland, Turkey, Saudi Arabia, Brazil, Ethiopia, and Indonesia. The global average energy system levelised cost of electricity gradually declines from 70 €/MWh in 2015 to 52 €/MWh in 2050 throughout the transition period, while deep decarbonisation of more than 95% around 2040, referenced to 2015, would be possible.The targets of the Paris Agreement can be well achieved in the power sector, while increasing societal welfare, given strong policy leadership.