The global carbon budget including fluxes of CO2 between atmosphere, land and ocean, and its atmospheric growth rate show large interannual to decadal variations. Yet, these variations are poorly represented in uninitialized simulations. In a novel approach we reconstruct and predict the global carbon cycle with the decadal prediction system based on the Max Planck Institute Earth system model (MPI-ESM) extended with an interactive carbon cycle. By assimilating atmospheric and oceanic data products into the MPI-ESM, we can well reproduce historical global carbon budget variations with high correlations relative to the assessments from the global carbon project of 0.75, 0.75 and 0.97 for atmospheric CO2 growth, air-land CO2 fluxes and air-sea CO2 fluxes, respectively. Retrospective predictions initializing from the assimilation simulation show the predictive skill of the air-sea CO2 fluxes up to 5 years, and the air-land CO2 fluxes and atmospheric carbon growth rate of 2 years.