Cost degression in photovoltaics, wind-power and battery storage has been faster than previously anticipated. In the future, climate policy to limit global warming to 1.5–2 °C will make carbon-based fuels increasingly scarce and expensive. Here we show that further progress in solar- and wind-power technology along with carbon pricing to reach the Paris Climate targets could make electricity cheaper than carbon-based fuels. In combination with demand-side innovation, for instance in e-mobility and heat pumps, this is likely to induce a fundamental transformation of energy systems towards a dominance of electricity-based end uses. In a 1.5 °C scenario with limited availability of bioenergy and carbon dioxide removal, electricity could account for 66% of final energy by mid-century, three times the current levels and substantially higher than in previous climate policy scenarios assessed by the Intergovernmental Panel on Climate Change. The lower production of bioenergy in our high-electrification scenarios markedly reduces energy-related land and water requirements. The impact of rapidly falling costs of renewable energy and battery technology on long-term climate stabilization pathways is not well understood. Luderer et al. show that reduced renewable costs and climate policies will make electricity the cheapest energy carrier and can lead to electricity accounting for nearly two-thirds of global energy use by mid-century.