The field capacity (FC) and permanent wilting point (PWP) are fundamental hydrological properties critical for assessing water availability within soils, rather than direct measures of soil health. Due to the challenges associated with their field measurement, alternative assessment methods are necessary. In this study, global-scale accessible soil data were retrieved from the world soil database called the World Soil Information Service (WoSIS), and artificial neural network (ANN) and gene-expression programming (GEP) algorithms were used to predict soil FC and PWP based on easily obtainable parameters from the database. The best-fit variable combination for FC (longitude, latitude, altitude, sand content, silt content, clay content, and electrical conductivity) and PWP (best-fit FC combination plus pH) modeling was determined. Both ANN and GEP showed greater accuracy than linear-based models in simulating the FC and PWP from the best-fit variables. The mean absolute error (MAE) was reduced by 51.54% for the FC and 56.38% for the PWP by the ANN model, compared with the linear model used in the previous literature. The normalized root mean square error (NRMSE) evaluation indicated that the ANN model performed best for PWP prediction (NRMSE of 19.9%), while the GEP model was superior for FC prediction (NRMSE of 29.9%). Between the ANN and GEP models, the ANN model showed a slightly higher model of interpretability; however, the GEP model exhibited a similar or better ability to avoid large error, based on the error distribution. Overall, our results demonstrated that machine learning is effective in predicting the FC and PWP from easily accessible data from WoSIS, and the GEP model is more preferable for FC and PWP modeling.