Copper (Cu) is an important micronutrient for marine organisms, which can also be toxic at elevated concentrations. Here, we present a new model of global ocean Cu biogeochemical cycling, constrained by GEOTRACES observations, with key processes including sources from rivers, dust, and sediments, biological uptake and remineralization of Cu, reversible scavenging of Cu onto sinking particles, conversion of Cu between labile and inert species, and ocean circulation. In order for the model to match observations, in particular the relatively small increase in Cu concentrations along the global “conveyor belt,” we find it is necessary to include significant external sources of Cu with a magnitude of roughly 1.3 Gmol yr−1, having a relatively stronger impact on the Atlantic Ocean, though the relative contributions of river, dust, and sediment sources are poorly constrained. The observed nearly linear increase in Cu concentrations with depth requires a strong benthic source of Cu, which includes the sedimentary release of Cu that was reversibly scavenged from the water column. The processes controlling Cu cycling in the Arctic Ocean appear to be unique, requiring both relatively high Cu concentrations in Arctic rivers and reduced scavenging in the Arctic. Observed partitioning of Cu between labile and inert phases is reproduced in the model by the slow conversion of labile Cu to inert in the whole water column with a half‐life of ∼250 years, and the photodegradation of inert Cu to labile in the surface ocean with a minimum half‐life of ∼2 years at the equator.