Accurate determination of average vehicle delays is significant for effective management of a signalized intersection. The vehicle delays can be determined by field studies, however, this approach is costly and time consuming. Analytical methods which are commonly utilized to estimate delay cannot generate accurate estimates, especially in oversaturated traffic flow conditions. Delay estimation models based on artificial intelligence have been presented in the literature in recent years to estimate the delay more accurately. However, the number of artificial/heuristic intelligence techniques utilized for vehicle delay estimation is limited in the literature. In this study, estimation models are developed using four different machine learning methods—support vector regression (SVR), random forest (RF), k nearest neighbor (kNN), and extreme gradient boosting (XGBoost)—that have not previously been applied in the literature for vehicle delay estimation at signalized intersections. The models were tested with data collected from 12 signalized intersections located in Ankara, the capital of Turkey, and the performance of the models was revealed. The models were furthermore compared with successful delay models from the literature. The developed models, in particular the RF and XGBoost models, showed high performance in estimating the delay at signalized intersections under different traffic conditions. The results indicate that the delay estimation models based on the RF and XGBoost techniques can significantly contribute to both the literature and practice.