Traffic prediction targets forecasting future traffic conditions using historical traffic data, serving a critical role in urban computing and transportation management. To mitigate the scarcity of traffic data while maintaining data privacy, numerous Federated Traffic Knowledge Transfer (FTT) approaches have been developed, which use transfer learning and federated learning to transfer traffic knowledge from data-rich cities to data-scarce cities, enhancing traffic prediction capabilities for the latter. However, current FTT approaches face challenges such as privacy leakage, cross-city data distribution discrepancies, low data quality, and inefficient knowledge transfer, limiting their privacy protection, effectiveness, robustness, and efficiency in real-world applications. To this end, we propose FedTT, an effective, efficient, and privacy-aware cross-city traffic knowledge transfer framework that transforms the traffic data domain from the data-rich cities and trains traffic models using the transformed data for the data-scarce cities. First, to safeguard data privacy, we propose a traffic secret transmission method that securely transmits and aggregates traffic domain-transformed data from source cities using a lightweight secret aggregation approach. Second, to mitigate the impact of traffic data distribution discrepancies on model performance, we introduce a traffic domain adapter to uniformly transform traffic data from the source cities' domains to that of the target city. Third, to improve traffic data quality, we design a traffic view imputation method to fill in and predict missing traffic data. Finally, to enhance transfer efficiency, FedTT is equipped with a federated parallel training method that enables the simultaneous training of multiple modules. Extensive experiments using 4 real-life datasets demonstrate that FedTT outperforms the 14 state-of-the-art baselines.