Cardiac induction requires stepwise integration of BMP and WNT pathway activity. Human embryonic stem cells (hESCs) are developmentally and clinically relevant for studying the poorly understood molecular mechanisms downstream of these cascades. We show that BMP and WNT signaling drive cardiac specification by removing sequential roadblocks that otherwise redirect hESC differentiation toward competing fates, rather than activating a cardiac program per se. First, BMP and WNT signals pattern mesendoderm through cooperative repression of SOX2, a potent mesoderm antagonist. BMP signaling promotes miRNA-877 maturation to induce SOX2 mRNA degradation, while WNT-driven EOMES induction transcriptionally represses SOX2. Following mesoderm formation, cardiac differentiation requires inhibition of WNT activity. We found that WNT inhibition serves to restrict expression of anti-cardiac regulators MSX1 and CDX2/1. Conversely, their simultaneous disruption partially abrogates the requirement for WNT inactivation. These results suggest that human cardiac induction depends on multi-stage repression of alternate lineages, with implications for deriving expandable cardiac stem cells.