Transformers have increasingly outperformed gated RNNs in obtaining new state-of-the-art results on supervised tasks involving text sequences. Inspired by this trend, we study the question of how Transformer-based models can improve the performance of sequential decision-making agents. We present the Working Memory Graph (WMG), an agent that employs multi-head self-attention to reason over a dynamic set of vectors representing observed and recurrent state. We evaluate WMG in three environments featuring factored observation spaces: a Pathfinding environment that requires complex reasoning over past observations, BabyAI gridworld levels that involve variable goals, and Sokoban which emphasizes future planning. We find that the combination of WMG's Transformer-based architecture with factored observation spaces leads to significant gains in learning efficiency compared to baseline architectures across all tasks. WMG demonstrates how Transformer-based models can dramatically boost sample efficiency in RL environments for which observations can be factored.