Hydrological and climatic modeling of near-surface water and energy fluxes is critically dependent on the availability of soil hydraulic parameters. Key among these parameters is the soil water characteristic curve (SWCC), a function relating soil water content (θ) to matric potential (ψ). The direct measurement of SWCC is laborious, hence, reported values of SWCC are spatially sparse and usually have only a small number of data pairs (θ, ψ) per sample. Pedotransfer function (PTF) models have been used to correlate SWCC with basic soil properties, but evidence suggests that SWCC is also shaped by vegetation-promoted soil structure and climate-modified clay minerals. To capture these effects in their spatial context, a machine learning framework (denoted as Covariate-based GeoTransfer Functions, CoGTFs) was trained using (a) a novel and comprehensive global dataset of SWCC parameters and (b) global maps of environmental covariates and soil properties at 1 km spatial resolution. Two CoGTF models were developed: one model (CoGTF-1) was based on predicted soil covariates because measured soil data are not generally available, and the other (CoGTF-2) used measured soil properties to model SWCC parameters. The spatial cross-validation of CoGTF-1 resulted, for the predicted van Genuchten SWCC parameters, in concordance correlation coefficients (CCC) of 0.321–0.565. To validate the resulting global maps of SWCC parameters and to compare the CoGTF framework to two pedotransfer functions from the literature, the predicted water contents at 0.1 m, 3.3 m, and 150 m matric potential were evaluated. The accuracy metrics for CoGTF were considerably better than PTF-based maps.