In the last decade, global cloud wide-area networks (WANs) have grown 10$\times$ in size due to the deployment of new network sites and datacenters, making it challenging for commercial optimization engines to solve the network traffic engineering (TE) problem within the temporal budget of a few minutes. In this work, we show that carefully designed deep learning models are key to accelerating the running time of intra-WAN TE systems for large deployments since deep learning is both massively parallel and it benefits from the wealth of historical traffic allocation data from production WANs. However, off-the-shelf deep learning methods fail to perform well on the TE task since they ignore the effects of network connectivity on flow allocations. They are also faced with a tractability challenge posed by the large problem scale of TE optimization. Moreover, neural networks do not have mechanisms to readily enforce hard constraints on model outputs (e.g., link capacity constraints). We tackle these challenges by designing a deep learning-based TE system -- Teal. First, Teal leverages graph neural networks (GNN) to faithfully capture connectivity and model network flows. Second, Teal devises a multi-agent reinforcement learning (RL) algorithm to process individual demands independently in parallel to lower the problem scale. Finally, Teal reduces link capacity violations and improves solution quality using the alternating direction method of multipliers (ADMM). We evaluate Teal on traffic matrices of a global commercial cloud provider and find that Teal computes near-optimal traffic allocations with a 59$\times$ speedup over state-of-the-art TE systems on a WAN topology of over 1,500 nodes.