This study develops new data-driven models using artificial neural networks (ANN) and gene expression programming (GEP) to estimate the ultimate load-bearing capacity of reinforced concrete (RC) columns retrofitted with carbon fiber-reinforced polymer (CFRP) wraps under eccentric loading conditions. A comprehensive database of 130 experimental specimens was assembled, comprising variables such as column diameter, eccentricity ratio, column height, longitudinal steel reinforcement details, unconfined concrete strength, FRP confinement levels, and lateral steel confinement. The GEP and ANN models were systematically trained and tested on this database. The model's performance was thoroughly assessed through the use of statistical metrics such as root mean squared error, mean absolute error, relative errors, and coefficients of determination. Sensitivity analysis identified the most influential input parameters on the model predictions. The results demonstrated the effectiveness of the data-driven ANN and GEP approaches for this structural engineering problem. The GEP model achieved an average prediction error of 16.707%, with the FRP strengthening index, column diameter, eccentricity ratio, steel reinforcement area, and column height being the most critical inputs based on sensitivity analysis. The ANN model performed even better with only 3.504% average error, showing the greatest sensitivity to the column diameter. While both models captured the key trends from input variations, the ANN exhibited more non-linear response characteristics compared to GEP. Benchmarking against existing theoretical models further confirmed the superiority and improved accuracy of the developed ANN and GEP models for estimating the load-bearing capacity of eccentrically-loaded, CFRP-confined RC columns.