Deep neural networks continue to show improved performance with increasing depth, an encouraging trend that implies an explosion in the possible permutations of network architectures and hyperparameters for which there is little intuitive guidance. To address this increasing complexity, we propose Evolutionary DEep Networks (EDEN), a computationally efficient neuro-evolutionary algorithm which interfaces to any deep neural network platform, such as TensorFlow. We show that EDEN evolves simple yet successful architectures built from embedding, 1D and 2D convolutional, max pooling and fully connected layers along with their hyperparameters. Evaluation of EDEN across seven image and sentiment classification datasets shows that it reliably finds good networks -- and in three cases achieves state-of-the-art results -- even on a single GPU, in just 6-24 hours. Our study provides a first attempt at applying neuro-evolution to the creation of 1D convolutional networks for sentiment analysis including the optimisation of the embedding layer.