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Alzheimer's disease is an incurable neurological disorder that leads to a gradual decline in cognitive abilities, but early detection can significantly mitigate symptoms. The automatic diagnosis of Alzheimer's disease is more important due to the shortage of expert medical staff, because it reduces the burden on medical staff and enhances the results of diagnosis. A detailed analysis of specific brain disorder tissues is required to accurately diagnose the disease via segmented magnetic resonance imaging (MRI). Several studies have used the traditional machine-learning approaches to diagnose the disease from MRI, but manual extracted features are more complex, time-consuming, and require a huge amount of involvement from expert medical staff. The traditional approach does not provide an accurate diagnosis. Deep learning has automatic extraction features and optimizes the training process. The Magnetic Resonance Imaging (MRI) Alzheimer's disease dataset consists of four classes: mild demented (896 images), moderate demented (64 images), non-demented (3200 images), and very mild demented (2240 images). The dataset is highly imbalanced. Therefore, we used the adaptive synthetic oversampling technique to address this issue. After applying this technique, the dataset was balanced. The ensemble of VGG16 and EfficientNet was used to detect Alzheimer's disease on both imbalanced and balanced datasets to validate the performance of the models. The proposed method combined the predictions of multiple models to make an ensemble model that learned complex and nuanced patterns from the data. The input and output of both models were concatenated to make an ensemble model and then added to other layers to make a more robust model. In this study, we proposed an ensemble of EfficientNet-B2 and VGG-16 to diagnose the disease at an early stage with the highest accuracy. Experiments were performed on two publicly available datasets. The experimental results showed that the proposed method achieved 97.35% accuracy and 99.64% AUC for multiclass datasets and 97.09% accuracy and 99.59% AUC for binary-class datasets. We evaluated that the proposed method was extremely efficient and provided superior performance on both datasets as compared to previous methods.