Floods can be very destructive causing heavy damage to life, property, and livelihoods. Global climate change and the consequent sea-level rise have increased the occurrence of extreme weather events, resulting in elevated and frequent flood risk. Therefore, accurate and timely flood forecasting in coastal river systems is critical to facilitate good flood management. However, the computational tools currently used are either slow or inaccurate. In this paper, we propose a Flood prediction tool using Graph Transformer Network (FloodGTN) for river systems. More specifically, FloodGTN learns the spatio-temporal dependencies of water levels at different monitoring stations using Graph Neural Networks (GNNs) and an LSTM. It is currently implemented to consider external covariates such as rainfall, tide, and the settings of hydraulic structures (e.g., outflows of dams, gates, pumps, etc.) along the river. We use a Transformer to learn the attention given to external covariates in computing water levels. We apply the FloodGTN tool to data from the South Florida Water Management District, which manages a coastal area prone to frequent storms and hurricanes. Experimental results show that FloodGTN outperforms the physics-based model (HEC-RAS) by achieving higher accuracy with 70% improvement while speeding up run times by at least 500x.