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This paper presents the response to anthropogenic forcing in the GISS‐E2.1 climate models for the 21st century Shared Socioeconomic Pathways emission scenarios within the Coupled Model Intercomparison Project Phase 6 (CMIP6). The experiments were performed using an updated and improved version of the NASA Goddard Institute for Space Studies (GISS) coupled general circulation model that includes two different versions for atmospheric composition: A non‐interactive version (NINT) with prescribed composition and a tuned aerosol indirect effect and the One‐Moment Aerosol model (OMA) version with fully interactive aerosols which includes a parameterized first indirect aerosol effect on clouds. The effective climate sensitivities are 3.0°C and 2.9°C for the NINT and OMA models, respectively. Each atmospheric version is coupled to two different ocean general circulation models: The GISS ocean model (E2.1‐G) and HYCOM (E2.1‐H). We describe the global mean responses for all future scenarios and spatial patterns of change for surface air temperature and precipitation for four of the marker scenarios: SSP1‐2.6, SSP2‐4.5, SSP4‐6.0, and SSP5‐8.5. By 2100, global mean warming ranges from 1.5°C to 5.2°C relative to 1,850–1,880 mean temperature. Two high‐mitigation scenarios SSP1‐1.9 and SSP1‐2.6 limit the surface warming to below 2°C by the end of the 21st century, except for the NINT E2.1‐H model that simulates 2.2°C of surface warming. For the high emission scenario SSP5‐8.5, the range is 4.6–5.2°C at 2100. Due to about 15% larger effective climate sensitivity and stronger transient climate response in both NINT and OMA CMIP6 models compared to CMIP5 versions, there is a stronger warming by 2100 in the SSP emission scenarios than in the comparable Representative Concentration Pathway (RCP) scenarios in CMIP5. Changes in sea ice area are highly correlated to global mean surface air temperature anomalies and show steep declines in both hemispheres, with the largest sea ice area decreases occurring during September in the Northern Hemisphere in both E2.1‐G (−1.21 × 106 km2/°C) and E2.1‐H models (−0.94 × 106 km2/°C). Both coupled models project decreases in the Atlantic overturning stream function by 2100. The largest decrease of 56%–65% in the 21st century overturning stream function is produced in the warmest scenario SSP5‐8.5 in the E2.1‐G model, comparable to the reduction in the corresponding CMIP5 GISS‐E2 RCP8.5 simulation. Both low‐end scenarios SSP1‐1.9 and SSP1‐2.6 also simulate substantial reductions of the overturning (9%–37%) with slow recovery of about 10% by the end of the 21st century (relative to the maximum decrease at the middle of the 21st century). Plain Language Summary: The projections of future climate change are uncertain because they are dependent on different possible scenarios of human‐caused emissions and their interaction with natural forcings, internal climate variability, and inter‐model differences. This paper presents the results of the climate model of the NASA Goddard Institute for Space Studies, GISS‐E2.1, for the anthropogenically forced climate response for the twenty first century Shared Socioeconomic Pathways emission scenarios within the Coupled Model Intercomparison Project Phase 6 (CMIP6). The sensitivity of the model response to different magnitudes of anthropogenic forcings in the twenty‐first‐century scenarios were performed using two different versions for the atmospheric composition and two different ocean general circulation models. Compared to CMIP5 GISS‐E2 versions, the CMIP6 GISS‐E2.1 climate model shows a stronger warming by 2100 in comparable scenarios due to larger effective climate sensitivity and transient climate response. Both climate models with two different ocean components project decreases in the Atlantic overturning stream function by 2100. Key Points: GISS E2.1 model with different configurations is used to carry out 134 Shared Socioeconomic Pathway (SSP) experimentsGISS‐E2.1 climate model shows a stronger warming by 2,100 in comparable Representative Concentration Pathway scenarios in CMIP5 due to larger effective climate sensitivity and stronger transient climate responseBoth coupled models, E2.1‐G and E2.1‐H, project decreases in the Atlantic overturning stream function by 2100 with the largest decrease in the warmest scenario SSP5‐8.5 in the E2.1‐G model [ABSTRACT FROM AUTHOR]