Abstract The arrival time prediction of coronal mass ejections (CMEs) is an area of active research. Many methods with varying levels of complexity have been developed to predict CME arrival. However, the mean absolute error (MAE) of predictions remains above 12 hr, even with the increasing complexity of methods. In this work we develop a new method for CME arrival time prediction that uses magnetohydrodynamic simulations involving data-constrained flux-rope-based CMEs, which are introduced in a data-driven solar wind background. We found that for six CMEs studied in this work the MAE in arrival time was ∼8 hr. We further improved our arrival time predictions by using ensemble modeling and comparing the ensemble solutions with STEREO-A and STEREO-B heliospheric imager data. This was done by using our simulations to create synthetic J-maps. A machine-learning (ML) method called the lasso regression was used for this comparison. Using this approach, we could reduce the MAE to ∼4 hr. Another ML method based on the neural networks (NNs) made it possible to reduce the MAE to ∼5 hr for the cases when HI data from both STEREO-A and STEREO-B were available. NNs are capable of providing similar MAE when only the STEREO-A data are used. Our methods also resulted in very encouraging values of standard deviation (precision) of arrival time. The methods discussed in this paper demonstrate significant improvements in the CME arrival time predictions. Our work highlights the importance of using ML techniques in combination with data-constrained magnetohydrodynamic modeling to improve space weather predictions.