Remaining useful life (RUL) prediction plays a core role in industrial prognostics and health management (PHM), requiring data-driven models with higher predictive capability for accurate long time series prediction. Developing reliable deep learning-based models based on multi-sensor monitoring data is fundamental for accurately predicting vibration trends during bearing operation and is crucial for bearing fault diagnosis and RUL prediction. In this work, a method for constructing a health index based on vibration signal is developed to describe the performance features of rolling bearings, which mainly includes feature extraction, sensitive feature index selection, dimensionality reduction, and normalization methods. In addition, a new RUL prediction method, TCN–Transformer, is developed which can efficiently learn and integrate local and global features of vibration signals, addressing the long time series prediction problem in RUL prediction. The TCN extracts local features, while the Transformer learns global features, both of which are seamlessly integrated through a specially designed feature fusion attention module. Both the health indicator (HI) constructed from extracted time domain and frequency domain feature parameters and the RUL prediction method were rigorously validated using the IEEE PHM 2012 Data Challenge dataset for rolling bearing prognostics. By employing the proposed HI construction method, the average comprehensive bearing performance index, used to evaluate RUL prediction accuracy, is improved by 8.69% across the entire dataset compared to the original feature-based composite index. The proposed RUL prediction model can more accurately predict the RUL of rolling bearings under different conditions, reducing the RMSE and MAE by 14.62% and 9.26%, respectively, and improving the SCORE by 13.04%. These results underscore the efficacy and superiority of our approach in RUL prediction of rotating machinery across varying conditions.