The COVID-19 pandemic, which originated in December 2019 in the city of Wuhan, China, continues to have a devastating effect on the health and well-being of the global population. Currently, approximately 8.8 million people have already been infected and more than 465,740 people have died worldwide. An important step in combating COVID-19 is the screening of infected patients using chest X-ray (CXR) images. However, this task is extremely time-consuming and prone to variability among specialists owing to its heterogeneity. Therefore, the present study aims to assist specialists in identifying COVID-19 patients from their chest radiographs, using automated computational techniques. The proposed method has four main steps: (1) the acquisition of the dataset, from two public databases; (2) the standardization of images through preprocessing; (3) the extraction of features using a deep features-based approach implemented through the networks VGG19, Inception-v3, and ResNet50; (4) the classifying of images into COVID-19 groups, using eXtreme Gradient Boosting (XGBoost) optimized by particle swarm optimization (PSO). In the best-case scenario, the proposed method achieved an accuracy of 98.71%, a precision of 98.89%, a recall of 99.63%, and an F1-score of 99.25%. In our study, we demonstrated that the problem of classifying CXR images of patients under COVID-19 and non-COVID-19 conditions can be solved efficiently by combining a deep features-based approach with a robust classifier (XGBoost) optimized by an evolutionary algorithm (PSO). The proposed method offers considerable advantages for clinicians seeking to tackle the current COVID-19 pandemic.