Context. At GeV energies, the sky is dominated by the interstellar emission from the Galaxy. With limited statistics and spatial resolution, accurately separating point sources is therefore challenging. Aims. Here we present the first application of deep learning based algorithms to automatically detect and classify point sources from gamma-ray data. For concreteness we refer to this approach as AutoSourceID. Methods. To detect point sources, we utilized U-shaped convolutional networks for image segmentation and k-means for source clustering and localization. We also explored the Centroid-Net algorithm, which is designed to find and count objects. Using two algorithms allows for a cross check of the results, while a combination of their results can be used to improve performance. The training data are based on 9.5 years of exposure from The Fermi Large Area Telescope (Fermi-LAT) and we used source properties of active galactic nuclei (AGNs) and pulsars (PSRs) from the fourth Fermi-LAT source catalog in addition to several models of background interstellar emission. The results of the localization algorithm are fed into a classification neural network that is trained to separate the three general source classes (AGNs, PSRs, and FAKE sources). Results. We compared our localization algorithms qualitatively with traditional methods and find them to have similar detection thresholds. We also demonstrate the robustness of our source localization algorithms to modifications in the interstellar emission models, which presents a clear advantage over traditional methods. The classification network is able to discriminate between the three classes with typical accuracy of similar to 70%, as long as balanced data sets are used in classification training. We published online our training data sets and analysis scripts and invite the community to join the data challenge aimed to improve the localization and classification of gamma-ray point sources.