In this paper we develop a probabilistic assessment of the energy transition and economic consequences of limiting global warming by the end of the century to 1.5 degrees C. The assessment is made by applying a Monte Carlo analysis in MERGE-ETL, a technology rich integrated assessment model with endogenous learning. We assume a deterministic 1.5 degrees C target and uncertainty in other factors such as economic growth, resources, and technology costs. The distributions of these variables are obtained by the PROMETHEUS stochastic world energy model. The study assumes early actions and quantifies the market penetration of low carbon technologies, the emission pathways and the economic costs for an efficient reduction of greenhouse gas emissions such that the temperature limit is not exceeded. We find that achieving the 1.5 degrees C Paris target is technically feasible but it requires immediate and global action. Key pillars in the decarbonization of the energy system are large deployment of renewable energy, early retirement of fossil based power plants, energy efficiency and negative emission technologies. Furthermore, that the availability of biomass resources, the rapid decrease of the costs of renewables and improvements in energy efficiency are the factors with the largest effect on the cost of carbon.