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Breast cancer remains one of the most prevalent and deadly cancers worldwide, making accurate diagnosis critical for effective treatment. Histopathological image classification is a key task in medical diagnostics for cancer detection. This paper presents state-of-the-art performance in histopathological image classification of breast cancer using a novel approach with the Vision Transformer (ViT) model fine-tuned using the BreakHis dataset. The BreakHis dataset, comprising of 7,909 breast cancer histopathological images across various magnification levels, serves as a crucial benchmark for evaluating machine learning models in this domain. While previous works have explored the use of ViTs for this task, our approach fine-tunes a ViT pre-trained on ImageNet using the Ranger optimizer, achieving unprecedented performance. The experimental results show that our fine-tuned ViT model achieves an accuracy of 99.99%, precision of 99.98%, recall of 99.99%, F1 score of 99.99%, specificity of 100.00%, false discovery rate (FDR) of 0.00%, false negative rate (FNR) of 0.02%, false positive rate (FPR) of 0.00%, Matthews correlation coefficient (MCC) of 99.97%, and negative predictive value (NPV) of 99.96%. This model and approach represents the highest accuracy ever achieved for BreakHis binary classification in machine learning using any model, underscoring the potential of Vision Transformers to substantially enhance diagnostic accuracy in histopathological image analysis and improve clinical outcomes. Transfer learning was also performed on the BACH and a histopathological image dataset for breast invasive ductal carcinomas (IDC).