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Leaf dry mass per unit area (LMA), carboxylation capacity (Vcmax) and leaf nitrogen per unit area (Narea) and mass (Nmass) are key traits for plant functional ecology and ecosystem modelling. There is however no consensus about how these traits are regulated, or how they should be modelled. Here we confirm that observed leaf nitrogen across species and sites can be estimated well from observed LMA and Vcmax at 25°C (Vcmax25). We then test the hypothesis that global variations of both quantities depend on climate variables in specific ways that are predicted by leaf-level optimality theory, thus allowing both Narea to be predicted as functions of the growth environment. A new global compilation of field measurements was used to quantify the empirical relationships of leaf N to Vcmax25 and LMA. Relationships of observed Vcmax25 and LMA to climate variables were estimated, and compared to independent theoretical predictions of these relationships. Soil effects were assessed by analysing biases in the theoretical predictions. LMA was the most important predictor of Narea (increasing) and Nmass (decreasing). About 60% of global variation across species and sites in observed Narea, and 31% in Nmass, could be explained by observed LMA and Vcmax25. These traits, in turn, were quantitatively related to climate variables, with significant partial relationships similar or indistinguishable from those predicted by optimality theory. Predicted trait values explained 21% of global variation in observed site-mean Vcmax25, 43% in LMA and 31% in Narea. Predicted Vcmax25 was biased low on clay-rich soils but predicted LMA was biased high, with compensating effects on Narea. Narea was overpredicted on organic soils. Synthesis. Global patterns of variation in observed site-mean Narea can be explained by climate-induced variations in optimal Vcmax25 and LMA. Leaf nitrogen should accordingly be modelled as a consequence (not a cause) of Vcmax25 and LMA, both being optimized to t