The prediction of tool wear helps minimize costs and enhance product quality in manufacturing. While existing data-driven models using machine learning and deep learning have contributed to the accurate prediction of tool wear, they often lack generality and require substantial training data for high accuracy. In this paper, we propose a new data-driven model that uses Bayesian Regularized Artificial Neural Networks (BRANNs) to precisely predict milling tool wear. BRANNs combine the strengths and leverage the benefits of artificial neural networks (ANNs) and Bayesian regularization, whereby ANNs learn complex patterns and Bayesian regularization handles uncertainty and prevents overfitting, resulting in a more generalized model. We treat both process parameters and monitoring sensor signals as BRANN input parameters. We conducted an extensive experimental study featuring four different experimental data sets, including the NASA Ames milling dataset, the 2010 PHM Data Challenge dataset, the NUAA Ideahouse tool wear dataset, and an in-house performed end-milling of the Ti6Al4V dataset. We inspect the impact of input features, training data size, hidden units, training algorithms, and transfer functions on the performance of the proposed BRANN model and demonstrate that it outperforms existing state-of-the-art models in terms of accuracy and reliability.