Eye movements during text reading can provide insights about reading disorders. Via eye-trackers, we can measure when, where and how eyes move with relation to the words they read. Machine Learning (ML) algorithms can decode this information and provide differential analysis. This work developed DysLexML, a screening tool for developmental dyslexia that applies various ML algorithms to analyze fixation points recorded via eye-tracking during silent reading of children. It comparatively evaluated its performance using measurements collected in a systematic field study with 69 native Greek speakers, children, 32 of which were diagnosed as dyslexic by the official governmental agency for diagnosing learning and reading difficulties in Greece. We examined a large set of features based on statistical properties of fixations and saccadic movements and identified the ones with prominent predictive power, performing dimensionality reduction. Specifically, DysLexML achieves its best performance using linear SVM, with an a accuracy of 97 %, with a small feature set, namely saccade length, number of short forward movements, and number of multiply fixated words. Furthermore, we analyzed the impact of noise on the fixation positions and showed that DysLexML is accurate and robust in the presence of noise. These encouraging results set the basis for developing screening tools in less controlled, larger-scale environments, with inexpensive eye-trackers, potentially reaching a larger population for early intervention.