During early cardiogenesis, bilateral fields of mesenchymal heart progenitor cells (HPCs) move from the anterior lateral plate mesoderm to the ventral midline, undergoing a mesenchymal-to-epithelial transition (MET) en route to forming a single epithelial sheet. Through tracking of tissue-level deformations in the heart-forming region (HFR) as well as movement trajectories and traction generation of individual HPCs, we find that the onset of MET correlates with a peak in mechanical stress within the HFR and changes in HPC migratory behaviors. Small-molecule inhibitors targeting actomyosin contractility reveal a temporally specific requirement of bulk tissue compliance to regulate heart development and MET. Targeting mutant constructs to modulate contractility and compliance in the underlying endoderm, we find that MET in HPCs can be accelerated in response to microenvironmental stiffening and can be inhibited by softening. To test whether MET in HPCs was responsive to purely physical mechanical cues, we mimicked a high-stress state by injecting an inert oildroplet to generate high strain in the HFR, demonstrating that exogenously applied stress was sufficient to drive MET. MET-induced defects in anatomy result in defined functional lesions in the larval heart, implicating mechanical signaling and MET in the etiology of congenital heart defects. From this integrated analysis of HPC polarity and mechanics, we propose that normal heart development requires bilateral HPCs to undergo a critical behavioral and phenotypic transition on their way to the ventral midline, and that this transition is driven in response to the changing mechanical properties of their endoderm substrate.