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We present results from the NASA GISS ModelE2.1‐G‐CC Earth System Model with coupled climate‐carbon cycle simulations that were submitted to the sixth phase of the Coupled Model Intercomparison Project (CMIP6) Coupled Climate‐Carbon Cycle MIP (C4MIP). Atmospheric CO2 concentration and carbon budgets for the land and ocean in the historical simulations were generally consistent with observations. Low simulated atmospheric CO2 concentrations during 1850–1950 were due to excess uptake from prescribed land cover change, which erroneously replaced arid shrublands with higher biomass crops, and assumed high 2004 LAI values in vegetated lands throughout the historical simulation. At the end of the historical period, slightly higher simulated CO2 than observed resulted from the land being an insufficient net carbon sink, despite the net effect of CO2 fertilization and warming‐induced increases to leaf photosynthetic capacity. The global ocean carbon uptake agreed well with the observations with the largest discrepancies in the low latitudes. Future climate projection at 2091–2100 agreed with CMIP5 models in the northward shift, of temperate deciduous forest climate and expansion across Eurasia along 60°N latitude, and dramatic regional biome shifts from drying and warming in continental Europe. Carbon feedback parameters were largely similar to the CMIP5 model ensemble. For our model, the variation of land feedback parameters within the uncertainty arises from the fertilization feedback being less sensitive due to lack of increased vegetation growth, and the comparably more negative ocean carbon‐climate feedback is due to the large slowdown of the Atlantic overturning circulation. Plain Language Summary: The Earth's global carbon cycle traces surface‐atmosphere exchanges of CO2 by the ocean and the land, including both natural processes (photosynthesis, respiration, ecological dynamics, gas exchange, and atmospheric transport) and anthropogenic activities (fossil fuel emissions and land use change). Scientists synthesize current understanding of carbon cycle science in Earth System Models (ESMs), to simulate the most significant processes in a highly complex system and to quantify how the land and ocean carbon sources and sinks of atmospheric CO2 behave and how they will change in the future. The NASA GISS ModelE2.1‐G‐CC ESM couples the NASA Ocean Biogeochemistry Model (NOBM) in the ocean, the Ent Terrestrial Biosphere Model (Ent TBM) on land, and CO2 transport through the atmosphere and interactions with Earth's radiation. Here we describe experiments that were contributed to the Coupled Model Intercomparison Project 6 (CMIP6). Results indicate that GISS ModelE2.1 reproduces the large‐scale properties of the carbon cycle generally consistently with measured data. In future warmer climates, major regional biome changes will occur in temperate to subarctic climates. The land and the ocean become net sinks, but they will have reduced ability to take up additional CO2 and thereby ameliorate climate warming. Key Points: Observed CO2 and carbon stocks/fluxes were reproduced within uncertainties, with most of disagreements in transient land uptakeOcean carbon‐climate feedback is stronger and land feedback slightly less sensitive than CMIP5; other feedback parameters are comparableFuture climate shifts temperate/boreal transitions northward to ~60°N, extend temperate deciduous forest along ~60°N, and warm/dry Europe [ABSTRACT FROM AUTHOR]