With the recent advances in the deep learning field, the use of deep convolutional neural networks (DCNNs) in biomedical image processing becomes very encouraging. This paper presents a new classification model for breast cancer masses based on DCNNs. We investigated the use of transfer learning from AlexNet and GoogleNet pre-trained models to suit this task. We experimentally determined the best DCNN model for accurate classification by comparing different models, which vary according to the design and hyper-parameters. The effectiveness of these models were demonstrated using four mammogram databases. All models were trained and tested using a mammographic dataset from CBIS-DDSM and INbreast databases to select the best AlexNet and GoogleNet models. The performance of the two proposed models was further verified using images from Egyptian National Cancer Institute (NCI) and MIAS database. When tested on CBIS-DDSM and INbreast databases, the proposed AlexNet model achieved an accuracy of 100% for both databases. While, the proposed GoogleNet model achieved accuracy of 98.46% and 92.5%, respectively. When tested on NCI images and MIAS databases, AlexNet achieved an accuracy of 97.89% with AUC of 98.32%, and accuracy of 98.53% with AUC of 98.95%, respectively. GoogleNet achieved an accuracy of 91.58% with AUC of 96.5%, and accuracy of 88.24% with AUC of 94.65%, respectively. These results suggest that AlexNet has better performance and more robustness than GoogleNet. To the best of our knowledge, the proposed AlexNet model outperformed the latest methods. It achieved the highest accuracy and AUC score and the lowest testing time reported on CBIS-DDSM, INbreast and MIAS databases.