Rigid and affine registrations to a common template are the essential steps during pre-processing of brain structural magnetic resonance imaging (MRI) data. Manual quality control (QC) of these registrations is quite tedious if the data contains several thousands of images. Therefore, we propose a machine learning (ML) framework for fully automatic QC of these registrations via global and local computation of the similarity functions such as normalized cross-correlation, normalized mutual-information, and correlation ratio, and using these as features for training of different ML classifiers. To facilitate supervised learning, misaligned images are generated. A structural MRI dataset consisting of 215 subjects from autism brain imaging data exchange is used for 5-fold cross-validation and testing. ML models based on local costs performed better than the models with global costs. Local cost based random forest, and AdaBoost models reached testing F1-scores and balanced accuracies of 0.98 and 0.95 respectively for QC of both rigid and affine registrations.