Migraine is a neurological disorder that is associated with severe headaches and seriously affects the lives of patients. Diagnosing Migraine Disease (MD) can be laborious and time-consuming for specialists. For this reason, systems that can assist specialists in the early diagnosis of MD are important. Although migraine is one of the most common neurological diseases, there are very few studies on the diagnosis of MD, especially electroencephalogram (EEG)-and deep learning (DL)-based studies. For this reason, in this study, a new system has been proposed for the early diagnosis of EEG- and DL-based MD. In the proposed study, EEG signals obtained from the resting state (R), visual stimulus (V), and auditory stimulus (A) from 18 migraine patients and 21 healthy control (HC) groups were used. By applying continuous wavelet transform (CWT) and short-time Fourier transform (STFT) methods to these EEG signals, scalogram-spectrogram images were obtained in the time-frequency (T-F) plane. Then, these images were applied as inputs in three different convolutional neural networks (CNN) architectures (AlexNet, ResNet50, SqueezeNet) that proposed deep convolutional neural network (DCNN) models and classification was performed. The results of the classification process were evaluated, taking into account accuracy (acc.), sensitivity (sens.), specificity (spec.), and performance criteria, and the performances of the preferred methods and models in this study were compared. In this way, the situation, method, and model that showed the most successful performance for the early diagnosis of MD were determined. Although the classification results are close to each other, the resting state, CWT method, and AlexNet classifier showed the most successful performance (Acc: 99.74%, Sens: 99.9%, Spec: 99.52%). We think that the results obtained in this study are promising for the early diagnosis of MD and can be of help to experts.