One debatable issue in traffic safety research is that cognitive load by secondary tasks reduces primary task performance, i.e., driving. In this paper, the study adopted a version of the n-back task as a cognitively loading secondary task on the primary task i.e., driving; where drivers drove in three different simulated driving scenarios. This paper has taken a multimodal approach to perform ‘intelligent multivariate data analytics’ based on machine learning (ML). Here, k-nearest neighbour (k-NN), support vector machine (SVM) and random forest (RF) are used for driver cognitive load classification. Moreover, physiological measures have proven to be sophisticated in cognitive load identification, yet it suffers from confounding factors and noise. Therefore, this work uses multi-component signals, i.e., physiological measures and vehicular features to overcome that problem. Both multiclass and binary classifications have been performed to distinguish normal driving from cognitive load tasks. To identify the optimal feature set, two feature selection algorithms, i.e., Sequential Forward Floating Selection (SFFS) and Random Forest have been applied where out of 323 features, a sub-set of 42 features has been selected as the best feature subset. For the classification, the RF has shown better performance with F1-score of 0.75 and 0.80 than two other algorithms. Also, the result shows that using multicomponent features classifiers could classify better than using features from a single source.