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The ocean carbon sink plays a critical role in climate, absorbing anthropogenic carbon from the atmosphere and mitigating climate change. The sink shows significant variability on decadal timescales, but estimates from models and observations disagree with one another, raising uncertainty over the magnitude of the sink, its variability, and its driving mechanisms. There is a need to reconcile observationally-based estimates of air-sea CO₂ fluxes with those of the changing ocean carbon inventory in order to improve our understanding of the sink, and doing so requires knowledge of how carbon is transported within the interior by the ocean circulation. Here we employ a recently developed Optimal Transformation Method (OTM) that uses water mass theory to relate interior changes in tracer distributions to transports and mixing and boundary forcings, and extend its application to include carbon using synthetic data. We validate the method using model outputs from a biogeochemical state estimate, and test its ability to recover boundary carbon fluxes and interior transports consistent with changes in heat, salt and carbon. Our results show that OTM effectively reconciles boundary carbon fluxes with interior carbon distributions when given a range of prior fluxes. OTM shows considerable skill in its reconstructions, reducing root-mean-squared errors from biased priors between model ‘truth’ and reconstructed boundary carbon fluxes by up to 71 %, with bias of the reconstructions consistently ≤ 0.06 mol-Cm⁻² yr⁻¹ globally. Inter-basin transports of carbon also compare well with the model truth, with residuals < 0.25 Pg C yr⁻¹ for reconstructions …