Quantifying the risk of system failure is a key input to a risk-based decision-making process for the in-service integrity management of aging steel catenary risers (SCRs), which are prone to fatigue failure within the touchdown zone (TDZ). However, in practice the computational cost of assessing the probability of failure (POF) for SCRs is prohibitive. In this paper, we propose an efficient framework for quantifying the fatigue POF within the SCR TDZ by using the Bayesian machine learning technique adopting Gaussian Processes (GP) for regression. GP-based predictive models perform stochastic response prediction rapidly and are therefore attractive for rapid evaluation of the SCR fatigue POF. In this paper, we introduce innovative techniques for predicting fatigue damage profiles within the SCR TDZ generated by an irregular sea-state applied to the host vessel at its mean offset position, and for dimensionality reduction in the regression analysis. We utilize a realistic case study to demonstrate the framework, which consists of a representative 20″ SCR connected to a semi-submersible host vessel located in 950 m water depth. In addition, we use a site-specific 32-year hindcast wave data and 1-year measured current data, with associated statistical distributions, for the long-term fatigue loading conditions. We also employ numerical simulation and a random sampling technique to create simulation-based input and output datasets for training and testing of the derived probabilistic simulation-based surrogate. The results show that the proposed method is able to predict the fatigue life of the representative riser efficiently and accurately. Finally, we demonstrate the usefulness of the proposed method by rapidly generating the fatigue POF for the 20″ SCR considering the uncertainties associated with input loads, material properties, geometric parameters, and soil stiffness.