(1) Background: Growing evidence suggests that electroencephalography (EEG), recording the brain’s electrical activity, can be a promising diagnostic tool for Alzheimer’s disease (AD). The diagnostic biomarkers based on quantitative EEG (qEEG) have been extensively explored, but few of them helped clinicians in their everyday practice, and reliable qEEG markers are still lacking. The study aims to find robust EEG biomarkers and propose a systematic discrimination framework based on signal processing and computer-aided techniques to distinguish AD patients from normal elderly controls (NC). (2) Methods: In the proposed study, EEG signals were preprocessed firstly and Maximal overlap discrete wavelet transform (MODWT) was applied to the preprocessed signals. Variance, Pearson correlation coefficient, interquartile range, Hoeffding’s D measure, and Permutation entropy were extracted as the input of the candidate classifiers. The AD vs. NC discriminant performance of each model was evaluated and an automatic diagnostic framework was eventually developed. (3) Results: A classification procedure based on the extracted EEG features and linear discriminant analysis based classifier achieved the accuracy of 93.18 ± 3.65 (%), the AUC of 97.92 ± 1.66 (%), the F-measure of 94.06 ± 4.04 (%), separately. (4) Conclusions: The developed discrimination framework can identify AD from NC with high performance in a systematic routine.