In order to explore the effects of mesoscale eddies on marine biogeochemistry over climate timescales, global ocean biogeochemical general circulation models (OBGCMs) need at least to be run at a horizontal resolution of a 0.25°, the minimal resolution admitting eddies. However, their use is currently limited because of a prohibitive computational cost and storage requirements. To overcome this problem, an online coarsening algorithm is evaluated in the oceanic component (NEMO‐GELATO‐PISCES) of CNRM‐ESM2‐1. This algorithm allows to compute biogeochemical processes at a coarse resolution (0.75°) while inheriting most of the dynamical characteristics of the eddy‐admitting OBGCM (0.25°). Through the coarse‐graining process, the effective resolution of the ocean dynamics seen by the biogeochemical model is higher than that which would be obtained from an OBGCM run at 0.75°. In this context, we assess how much the increase from low (1°) to coarse‐grained horizontal resolution impacts the ocean dynamics and the marine biogeochemistry over long‐term climate simulations. The online coarsening reduces the computational cost by 60% with respect to that of the eddy‐admitting OBGCM. In addition, it improves the representation of chlorophyll, nutrients, oxygen, and sea‐air carbon fluxes over more than half of the open ocean area compared to the 1° OBGCM. Most importantly, the coarse‐grained OBGCM captures the physical‐biogeochemical coupling between sea‐air carbon fluxes and sea surface height and between oxygen minimum zone boundaries and eddies, as produced by the eddy‐admitting OBGCM. Such a cost‐efficient coarsening algorithm offers a good trade‐off to conduct process‐based studies over centennial timescales at higher resolution.