Plant functional traits (FTs) determine growth, reproduction and survival strategies of plants adapted to their growth environment. Exploring global geographic patterns of FTs, their covariation and their relationships to climate are necessary steps towards better-founded predictions of how global environmental change will affect ecosystem composition. We compile an extensive global dataset for 16 FTs and characterise trait-trait and trait-climate relationships separately within non-woody, woody deciduous and woody evergreen plant groups, using multivariate analysis and generalised additive models (GAMs). Among the six major FTs considered, two dominant trait dimensions—representing plant size and the leaf economics spectrum (LES) respectively—are identified within all three groups. Size traits (plant height, diaspore mass) however are generally higher in warmer climates, while LES traits (leaf mass and nitrogen per area) are higher in drier climates. Larger leaves are associated principally with warmer winters in woody evergreens, but with wetter climates in non-woody plants. GAM-simulated global patterns for all 16 FTs explain up to three-quarters of global trait variation. Global maps obtained by upscaling GAMs are broadly in agreement with iNaturalist citizen-science FT data. This analysis contributes to the foundations for global trait-based ecosystem modelling by demonstrating universal relationships between FTs and climate.