Path-tracking control is an integral part of motion planning in autonomous vehicles, where a control system on the vehicle will provide acceleration and steering angle commands to ensure accurate tracking of its longitudinal and lateral movements in reference to a pre-defined trajectory. In this paper, a scenario and machine learning-based data-driven control approach is proposed for a path-tracking controller. Firstly, a deep reinforcement learning (DRL) model is developed to facilitate the control of the vehicle's longitudinal speed. A deep deterministic policy gradient algorithm is employed to train the reinforcement learning model. The main objective of this model is to maintain a safe distance from a lead vehicle (if present) or track a velocity set by the driver. Secondly, a lateral steering controller is developed to control the steering angle of the vehicle with the main goal of following a reference trajectory. Finally, the longitudinal and lateral control models are coupled to obtain a complete path-tracking controller at a wide range of vehicle speeds. The state-of-the-art model-based path-tracking controller is also built (using the model predictive control and Stanley control) to evaluate the performance of the proposed model. The results showed that the performance of the proposed data-driven DRL control model is effective compared with model-based control approaches (in terms of the velocity error, lateral yaw angle error, and lateral distance error).