In the paper, the automated evolutionary approach FEDOT-NAS for the design of convolutional neural networks is proposed. It allows building object recognition models for remote sensing tasks. The comparison of the proposed approach with state-of-the-art tools for neural architecture search is conducted for several examples of satellite-related datasets. The results of the experiments confirm the correctness and effectiveness of the proposed approach. The implementation of FEDOT-NAS is available as an open-source tool.