This study evaluates the effect of climate uncertainties on the transformations in the global energy system needed for realizing mitigation targets in the long term. Climate uncertainties affect the amount of allowable emissions from human activities that are consistent with a given climate target, and, thus, the range of necessary energy transformations. A range of emission scenarios consistent with intermediate (RCP4.5) and stringent (RCP2.6) mitigation targets are analyzed with an integrated assessment model (IAM). Emission scenarios are generated with an earth system model of intermediate complexity, which evaluated the variability of allowable carbon emissions due to uncertainties in the climate sensitivity, the carbon cycle and its feedbacks. The results showed that even when climate uncertainties are reflected at different scales across energy supply components, achieving mitigation targets needs partial decarbonization of supply, scale up of carbon capture and storage (CCS), and decreased energy consumption. The effect of climate uncertainties was largest for coal without CCS (up to 100% in 2100 compared to the central scenario) and bioenergy with CCS (up to 23% in 2100 compared to the central scenario). Land for bioenergy feedstocks, and the deployment of unmanaged lands for other purposes also had a considerable variation (10-20% in 2100). Compared to the uncertainty in socio-economic factors quantified in IAMs, the variation induced by the climate uncertainties was small. In contrast to previous IAM studies, the results herein explicitly described how climate-related uncertainties affect the global energy system, based on scenarios incorporating a robust approach for covering a wide scope of uncertainties from a climate model.