When robots operate in real-world off-road environments with unstructured terrains, the ability to adapt their navigational policy is critical for effective and safe navigation. However, off-road terrains introduce several challenges to robot navigation, including dynamic obstacles and terrain uncertainty, leading to inefficient traversal or navigation failures. To address these challenges, we introduce a novel approach for adaptation by negotiation that enables a ground robot to adjust its navigational behaviors through a negotiation process. Our approach first learns prediction models for various navigational policies to function as a terrain-aware joint local controller and planner. Then, through a new negotiation process, our approach learns from various policies' interactions with the environment to agree on the optimal combination of policies in an online fashion to adapt robot navigation to unstructured off-road terrains on the fly. Additionally, we implement a new optimization algorithm that offers the optimal solution for robot negotiation in real-time during execution. Experimental results have validated that our method for adaptation by negotiation outperforms previous methods for robot navigation, especially over unseen and uncertain dynamic terrains.