Loop closure detection is important for simultaneous localization and mapping (SLAM), which associates current observations with historical keyframes, achieving drift correction and global relocalization. However, a falsely detected loop can be fatal, and this is especially difficult in repetitive environments where appearance-based features fail due to the high similarity. Therefore, verification of a loop closure is a critical step in avoiding false positive detections. Existing works in loop closure verification predominantly focus on learning invariant appearance features, neglecting the prior knowledge of the robot's spatial-temporal motion cue, i.e., trajectory. In this letter, we propose ROVER, a loop closure verification method that leverages the historical trajectory as a prior constraint to reject false loops in challenging repetitive environments. For each loop candidate, it is first used to estimate the robot trajectory with pose-graph optimization. This trajectory is then submitted to a scoring scheme that assesses its compliance with the trajectory without the loop, which we refer to as the trajectory prior, to determine if the loop candidate should be accepted. Benchmark comparisons and real-world experiments demonstrate the effectiveness of the proposed method. Furthermore, we integrate ROVER into state-of-the-art SLAM systems to verify its robustness and efficiency. Our source code and self-collected dataset are available atthis https URL.