Nitrous oxide (N2O) is a potent greenhouse gas (GHG) and ozone destructing agent; yet global estimates of N2O emissions are uncertain. Marine N2O stems from nitrification and denitrification processes which depend on organic matter cycling and dissolved oxygen (O2). We introduce N2O as an obligate intermediate product of denitrification and as an O2‐dependent by‐product from nitrification in the Bern3D ocean model. A large model ensemble is used to probabilistically constrain modern and to project marine N2O production for a low (Representative Concentration Pathway (RCP)2.6) and high GHG (RCP8.5) scenario extended to A.D. 10,000. Water column N2O and surface ocean partial pressure N2O data serve as constraints in this Bayesian framework. The constrained median for modern N2O production is 4.5 (±1σ range: 3.0 to 6.1) Tg N yr−1, where 4.5% stems from denitrification. Modeled denitrification is 65.1 (40.9 to 91.6) Tg N yr−1, well within current estimates. For high GHG forcing, N2O production decreases by 7.7% over this century due to decreasing organic matter export and remineralization. Thereafter, production increases slowly by 21% due to widespread deoxygenation and high remineralization. Deoxygenation peaks in two millennia, and the global O2 inventory is reduced by a factor of 2 compared to today. Net denitrification is responsible for 7.8% of the long‐term increase in N2O production. On millennial timescales, marine N2O emissions constitute a small, positive feedback to climate change. Our simulations reveal tight coupling between the marine carbon cycle, O2, N2O, and climate. Key Points A new parameterization for marine N2O production by nitrification and denitrification is developed Modern marine N2O emissions are constrained by observations to 4.3 (2.8 to 5.9) Tg N yr‐1 Probabilistic projections yield massive reductions in O2 and a long‐term increase in N2O emissions