The respiratory rate (RR) serves as a critical physiological parameter in the context of both diagnostic and prognostic evaluations. Due to the challenges of direct measurement, RR is still predominantly measured through the traditional manual counting-breaths method in clinic practice. Numerous algorithms and machine learning models have been developed to predict RR using physiological signals, such as electrocardiogram (ECG) or/and photoplethysmogram (PPG) signals. Yet, the accuracy of these existing methods on available datasets remains limited, and their prediction on new data is also unsatisfactory for actual clinical applications. In this paper, we proposed an enhanced Transformer model with inception blocks for predicting RR based on both ECG and PPG signals. To evaluate the generalization capability on new data, our model was trained and tested using subject-level ten-fold cross-validation using data from both BIDMC and CapnoBase datasets. On the test set, our model achieved superior performance over five popular deep-learning-based methods with mean absolute error (1.2) decreased by 36.5% and correlation coefficient (0.85) increased by 84.8% compared to the best results of these models. In addition, we also proposed a new pipeline to preprocess ECG and PPG signals to improve model performance. We believe that the development of the TransRR model is expected to further expedite the clinical implementation of automatic RR estimation.