In this paper, we focus on the Ego-Exo Object Correspondence task, an emerging challenge in the field of computer vision that aims to map objects across ego-centric and exo-centric views. We introduce ObjectRelator, a novel method designed to tackle this task, featuring two new modules: Multimodal Condition Fusion (MCFuse) and SSL-based Cross-View Object Alignment (XObjAlign). MCFuse effectively fuses language and visual conditions to enhance target object localization, while XObjAlign enforces consistency in object representations across views through a self-supervised alignment strategy. Extensive experiments demonstrate the effectiveness of ObjectRelator, achieving state-of-the-art performance on Ego2Exo and Exo2Ego tasks with minimal additional parameters. This work provides a foundation for future research in comprehensive cross-view object relation understanding highlighting the potential of leveraging multimodal guidance and cross-view alignment. Codes and models will be released to advance further research in this direction.