Deep learning architectures have received much attention in recent years demonstrating state-of-the-art performance in several segmentation, classification and other computer vision tasks. Most of these deep networks are based on either convolutional or fully convolutional architectures. In this paper, we propose a novel object-based deep-learning framework for semantic segmentation in very high-resolution satellite data. In particular, we exploit object-based priors integrated into a fully convolutional neural network by incorporating an anisotropic diffusion data preprocessing step and an additional loss term during the training process. Under this constrained framework, the goal is to enforce pixels that belong to the same object to be classified at the same semantic category. We compared thoroughly the novel object-based framework with the currently dominating convolutional and fully convolutional deep networks. In particular, numerous experiments were conducted on the publicly available ISPRS WGII/4 benchmark datasets, namely Vaihingen and Potsdam, for validation and inter-comparison based on a variety of metrics. Quantitatively, experimental results indicate that, overall, the proposed object-based framework slightly outperformed the current state-of-the-art fully convolutional networks by more than 1% in terms of overall accuracy, while intersection over union results are improved for all semantic categories. Qualitatively, man-made classes with more strict geometry such as buildings were the ones that benefit most from our method, especially along object boundaries, highlighting the great potential of the developed approach.