Over the last decades, back‐calculation (BC) techniques for ocean anthropogenic carbon (Cant) estimation have improved and evolved into different methodologies that are not exempt from various assumptions and limitations. No single optimal BC method exists to date for computing Cant; therefore, it is necessary to continue advancing the broad range of approaches. Here, we present a novel method based on the BC fundamentals that combines marine‐carbonate‐system (MCS) data and the Total Matrix Intercomparison (TMI) framework. This MCS‐TMI approach differs from other BC methods by using the TMI to reconstruct deep‐ocean biogeochemical properties and their preformed conditions. It also incorporates a global sea‐air oxygen disequilibrium term, and a dynamic stoichiometric carbon‐to‐oxygen ratio that depends on the water‐mass ideal time. The MCS‐TMI yields a total Cant inventory of 124 ± 7 Pg C (referred to 1995), in good agreement with previous global Cant climatologies. The MCS‐TMI method uncertainty (±5.6 μmol kg−1) is controlled by input‐data errors that, nonetheless, have a minimal impact on the total Cant inventory. In contrast, our total Cant inventory uncertainty is governed by methodological errors, specifically those related to the TMI's boundary conditions. Our study demonstrates the effectiveness of MCS data‐based climatologies in reconstructing a 3D gridded Cant climatology, and the validity of ocean circulation transport operators for obtaining BC preformed conditions.