Many NLP applications can be framed as a graph-to-sequence learning problem. Previous work proposing neural architectures on this setting obtained promising results compared to grammar-based approaches but still rely on linearisation heuristics and/or standard recurrent networks to achieve the best performance. In this work, we propose a new model that encodes the full structural information contained in the graph. Our architecture couples the recently proposed Gated Graph Neural Networks with an input transformation that allows nodes and edges to have their own hidden representations, while tackling the parameter explosion problem present in previous work. Experimental results show that our model outperforms strong baselines in generation from AMR graphs and syntax-based neural machine translation.