Current trends in networking propose the use of Machine Learning (ML) for a wide variety of network optimization tasks. As such, many efforts have been made to produce ML-based solutions for Traffic Engineering (TE), which is a fundamental problem in Internet Service Provider (ISP) networks. Nowadays, state-of-the-art TE optimizers rely on traditional optimization techniques, such as Local search, Constraint Programming, or Linear programming. In this paper, we present MAGNNETO, a distributed ML-based framework that leverages Multi-Agent Reinforcement Learning and Graph Neural Networks for distributed TE optimization. MAGNNETO deploys a set of agents across the network that learn and communicate in a distributed fashion via message exchanges between neighboring agents. Particularly, we apply this framework to optimize link weights in Open Shortest Path First (OSPF), with the goal of minimizing network congestion. In our evaluation, we compare MAGNNETO against several state-of-the-art TE optimizers in more than 75 topologies (up to 153 nodes and 354 links), including realistic traffic loads. Our experimental results show that, thanks to its distributed nature, MAGNNETO achieves comparable performance to state-of-the-art TE optimizers with significantly lower execution times. Moreover, our ML-based solution demonstrates a strong generalization capability to successfully operate in new networks unseen during training.