Tagged magnetic resonance imaging (MRI) is a widely used imaging technique for measuring tissue deformation in moving organs. Due to tagged MRI's intrinsic low anatomical resolution, another matching set of cine MRI with higher resolution is sometimes acquired in the same scanning session to facilitate tissue segmentation, thus adding extra time and cost. To mitigate this, in this work, we propose a novel dual-cycle constrained bijective VAE-GAN approach to carry out tagged-to-cine MR image synthesis. Our method is based on a variational autoencoder backbone with cycle reconstruction constrained adversarial training to yield accurate and realistic cine MR images given tagged MR images. Our framework has been trained, validated, and tested using 1,768, 416, and 1,560 subject-independent paired slices of tagged and cine MRI from twenty healthy subjects, respectively, demonstrating superior performance over the comparison methods. Our method can potentially be used to reduce the extra acquisition time and cost, while maintaining the same workflow for further motion analyses.