The global ocean Biological Carbon Pump (BCP) removes dissolved inorganic carbon (DIC) from the surface ocean through photosynthesis, driving more atmospheric CO₂ into the ocean. DIC is converted into organic forms of carbon during photosynthesis that cannot be exchanged with the atmosphere until it is decomposed. A small fraction of this organic matter produced by the BCP is exported, or sinks, to deeper ocean layers where it can remain sequestered away from the atmosphere for 10s-100s of years. As an important regulator of atmospheric CO₂ concentrations, it is necessary to quantify the BCP to enable predictions of future climate. We provide new constraints on key metrics describing the strength of the BCP, including total organic carbon export and export efficiency. Our data-constrained model quantifies the climatological average BCP by inverting dissolved oxygen measurements from the World Ocean Atlas using the Ocean Circulation Inverse Model (OCIM2). In our mass balance framework, total oxygen utilization from organic matter respiration at depth balances oxygen and organic matter production in the surface layer. Our climatological average inverse model provides new constraints on the BCP, offers a new resource for benchmarking forward models, and adds insight into the underlying equations governing BCP processes.