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While deep neural networks have been achieving state-of-the-art performance across a wide variety of applications, their vulnerability to adversarial attacks limits their widespread deployment for safety-critical applications. Alongside other adversarial defense approaches being investigated, there has been a very recent interest in improving adversarial robustness in deep neural networks through the introduction of perturbations during the training process. However, such methods leverage fixed, pre-defined perturbations and require significant hyper-parameter tuning that makes them very difficult to leverage in a general fashion. In this study, we introduce Learn2Perturb, an end-to-end feature perturbation learning approach for improving the adversarial robustness of deep neural networks. More specifically, we introduce novel perturbation-injection modules that are incorporated at each layer to perturb the feature space and increase uncertainty in the network. This feature perturbation is performed at both the training and the inference stages. Furthermore, inspired by the Expectation-Maximization, an alternating back-propagation training algorithm is introduced to train the network and noise parameters consecutively. Experimental results on CIFAR-10 and CIFAR-100 datasets show that the proposed Learn2Perturb method can result in deep neural networks which are $4-7\%$ more robust on $l_{\infty}$ FGSM and PDG adversarial attacks and significantly outperforms the state-of-the-art against $l_2$ $C\&W$ attack and a wide range of well-known black-box attacks.