360° videos offer a hyper-immersive experience that allows the viewers to explore a dynamic scene from full 360 degrees. To achieve more user-friendly and personalized content creation in 360° video format, we seek to lift standard perspective videos into 360° equirectangular videos. To this end, we introduce Imagine360, the first perspective-to-360° video generation framework that creates high-quality 360° videos with rich and diverse motion patterns from video-based control. Imagine360 learns fine-grained spherical visual and motion patterns from limited 360° video data with several key designs. 1) Firstly we adopt the dual-branch design, including a perspective and a panorama video denoising branch to provide local and global constraints for 360° video generation, with motion module and spatial LoRA layers fine-tuned on extended web 360° videos. 2)Additionally, an antipodal mask is devised to capture long-range motion dependencies, enhancing the reversed camera motion between antipodal pixels across hemispheres. 3) To handle general perspective video inputs, we propose elevation-aware designs that adapt to varying video masking due to changing elevations across frames. Extensive experiments show Imagine360 achieves superior graphics quality and motion coherence among state-of-the-art 360° video generation methods. We believe Imagine360 holds promise for advancing personalized, immersive 360° video creation.