Depression is a mental disorder that may lead to self-mutilation or suicide if left untreated. Selective serotonin reuptake inhibitors (SSRIs) and repetitive transcranial magnetic stimulation (rTMS) are among the most commonly prescribed therapies to treat depression. These therapies are prescribed and recommended to be taken over a period of time, and the main challenge is that about 50% of the patients might respond to these ways of treatments. In general, a psychiatric recommends one way of treatment based on his/her experience and waits for a period of time to evaluate the results. However, if the way of treatment is unsuccessful to decrease the depression level that might increase the risk of self-mutilation or suicide. This paper proposes a robust software called University of North Texas-Atieh Hospital (UNT-AT) to predict the outcomes of two different therapies for depressed patients based on recorded electroencephalogram (EEG) signals. The UNT-AT software utilizes phase space reconstruction (PSR) of EEG signals, a robust chaotic technique for tracking the brain’s nonlinear dynamics, along with novel geometrical features (GFs) to decode the complex behavior of EEG signals. Initially, PSR of EEG signals is plotted in two-dimensional space, and GFs are used to quantify the PSR shape. Statistically significant features are selected using the Kruskal-Wallis test and are then fed into traditional machine learning algorithms and artificial neural network architectures for classification using 10-fold cross-validations to avoid bias. The UNT-AT software is evaluated using two different databases for SSRI and rTMS therapies, including data from 30 and 15 depressed patients, respectively. The results show that our proposed software achieves classification accuracies of 94.14% and 97.67% for predicting therapy outcomes for SSRI and rTMS, respectively. Our proposed software is the first system in literature to be used to choose the best course of treatments for depressed patients. The software is efficient and can be used in clinics and hospitals to assist neurologists and psychiatrists in prescribing the most effective course of treatment for depression.