A correct quantification of mass and energy exchange processes among Earth's land surface, groundwater, and atmosphere requires an accurate parameterization of soil hydraulic properties. Pedotransfer functions (PTFs) are useful in this regard because they estimate these otherwise difficult to obtain characteristics using texture and other ubiquitous soil data. Most PTFs estimate parameters of empirical hydraulic functions with modest accuracy. In a continued pursuit of improving global‐scale PTF estimates, we evaluated whether improvements can be obtained when estimating parameters of hydraulic functions that make physically based assumptions. To this end, we developed a PTF that estimates the parameters of the Kosugi retention and hydraulic conductivity functions (Kosugi, 1994, https://doi.org/10.1029/93WR02931, 1996, https://doi.org/10.1029/96WR01776), which explicitly assume a lognormal pore size distribution and apply the Young‐Laplace equation to derive a corresponding pressure head distribution. Using a previously developed combination of machine learning and bootstrapping, the developed five hierarchical PTFs allow for estimates under practical data‐poor to data‐rich conditions. Using an independent global data set containing nearly 50,000 samples (118,000 retention points), we demonstrated that the new Kosugi‐based PTFs outperformed two van Genuchten‐based PTFs calibrated on the same data. The new PTFs were applied to a 1 × 1 km² global map of texture and bulk density, thus producing maps of the parameters, field capacity, wilting point, plant available water, and associated uncertainties. Soil hydraulic parameters exhibit a much larger variability in the Northern Hemisphere than in the Southern Hemisphere, which is likely due to the geographical distribution of climate zones that affect weathering and sedimentation processes.