Numerous ongoing and future large area surveys (e.g. DES, EUCLID, LSST, WFIRST), will increase by several orders of magnitude the volume of data that can be exploited for galaxy morphology studies. The full potential of these surveys can only be unlocked with the development of automated, fast and reliable analysis methods. In this paper we present DeepLeGATo, a new method for two-dimensional photometric galaxy profile modeling, based on convolutional neural networks. Our code is trained and validated on analytic profiles (HST/CANDELS F160W filter) and it is able to retrieve the full set of parameters of one- component S\'ersic models: total magnitude, effective radius, S\'ersic index, axis ratio. We show detailed comparisons between our code and GALFIT. On simulated data, our method is more accurate than GALFIT and 3000 time faster on GPU (50 times when run on the same CPU). On real data, DeepLeGATo trained on simulations behaves similarly to GALFIT on isolated galaxies. With a fast domain adaptation step made with the 0.1 - 0.8 per cent the size of the training set, our code is easily capable to reproduce the results obtained with GALFIT even on crowded regions. DeepLeGATo does not require any human intervention beyond the training step, rendering it much automated than traditional profiling methods. The development of this method for more complex models (two-component galaxies, variable PSF, dense sky regions) could constitute a fundamental tool in the era of big data in astronomy.