Anthropogenic climate change will drive extensive mass loss across both the Antarctic (AIS) and Greenland Ice Sheets (GrIS), with the potential for feedbacks on the global climate system, especially in polar regions. Historically, the high latitude North Atlantic and Southern Ocean have been the most critical regions for global anthropogenic heat and carbon uptake, but our understanding of how this uptake will be altered by future freshwater discharge is incomplete. Here, we assess each ice sheet’s impact on the global ocean storage of anthropogenic heat and carbon for a high-emission scenario over the 21$^{\textrm{st}}$ century using a coupled Earth system model. Notably, combined AIS and GrIS freshwater engenders distinct anthropogenic heat and carbon storage anomalies as the two diagnostics respond disparately in the high latitude Southern Ocean and North Atlantic. We explore the impact of contemporaneous mass loss from both ice sheets on anthropogenic heat and carbon storage and quantify the linear and nonlinear contributions of each ice sheet. We find that GrIS mass loss exerts a primary control on the 21$^{st}$-century evolution of both global oceanic heat and carbon storage, with AIS impacts appearing after the 2080s. Non-linear impacts of simultaneous ice sheets’ discharge have a non-negligible contribution to the evolution of both heat and carbon storage. Further, anthropogenic heat changes are realized more quickly in response to ice sheet discharge than anthropogenic carbon. Our results highlight the need to incorporate both ice sheets actively in climate models in order to accurately project future global climate.