Preterm birth is associated with significant mortality and a risk for lifelong morbidity. The complex multifactorial aetiology hampers accurate prediction and thus optimal care. A pipeline consisting of bespoke machine learning methods for data imputation, feature selection, and regression models to predict gestational age (GA) at birth was developed and evaluated from comprehensive multi-modal morphological and functional fetal MRI data from 176 control cases and 67 preterm birth cases. The GA at birth predictions were classified into term and preterm categories and their accuracy, sensitivity, and specificity were reported. An ablation study was performed to further validate the design of the pipeline. The pipeline achieves an R2 score of 0.51 and a mean absolute error of 2.22 weeks. It also achieves a 0.88 accuracy, 0.86 sensitivity, and 0.89 specificity, outperforming previous classification efforts in the literature. The predominant features selected by the pipeline include cervical length and various placental T2* values. The confluence of fast, motion-robust and multi-modal fetal MRI techniques and machine learning prediction allowed the prediction of the gestation at birth. This information is essential for any pregnancy. To the best of our knowledge, preterm birth had only been addressed as a classification problem in the literature. Therefore, this work provides a proof of concept. Future work will increase the cohort size to allow for finer stratification within the preterm birth cohort.