We report on a data-driven approach for the remaining useful life (RUL) estimation of rolling element bearings based on ε-Support Vector Regression ( ε-SVR). Lifetime data are analyzed and evaluated. The occurrence of critical faults in every test is located, and a critical operational threshold is established. Multiple statistical features from the time-domain, frequency domain, and time-scale domain through a wavelet transform are extracted from the recordings of two accelerometers, and assessed for their diagnostic performance. Among those features, Wiener entropy is utilized for the first time in the condition monitoring of rolling bearings. A SVR model is trained and tested for the prediction of RUL on unseen data. Special attention is given in the tuning and the optimization of the user-defined hyper-parameters of the e-SVR model. Error bounds are estimated at each prediction point through a Bayesian treatment of the classical SVR model. The results are in good agreement to the actual RUL curve for all the tested cases. Prognostic performance metrics are also provided, and the discussion on the test results concludes with the generic character of the proposed methodology and its applicability in any prognostic task.