Quantifying the anthropogenic fluxes of CO2 is important to understand the evolution of carbon sink capacities, on which the required strength of our mitigation efforts directly depends. For the historical period, the global carbon budget (GCB) can be compiled from observations and model simulations as is done annually in the Global Carbon Project’s (GCP) carbon budgets. However, the historical budget only considers a single realization of the Earth system and cannot account for internal climate variability. Understanding the distribution of internal climate variability is critical for predicting the future carbon budget terms and uncertainties. We present here a decomposition of the GCB for the historical period and the RCP4.5 scenario using single model large ensemble simulations from the Max Planck Institute Grand Ensemble (MPI-GE) to capture internal variability. We calculate uncertainty ranges for the natural sinks and anthropogenic emissions that arise from internal climate variability, and by using this distribution, we investigate the likelihood of historical fluxes with respect to plausible climate states. Our results show these likelihoods have substantial fluctuations due to internal variability, which are partially related to ENSO. We find that the largest internal variability in the MPI-GE stems from the natural land sink and its increasing carbon stocks over time. The allowable fossil fuel emissions consistent with 3°C warming may be between 9–18 PgCyr-1. The MPI-GE is generally consistent with GCP’s global budgets with the notable exception of land-use change emissions in recent decades, highlighting that human action is inconsistent with climate mitigation goals.