Collective migration of cohesive tissues is a fundamental process in morphogenesis and is particularly well illustrated during gastrulation by the rapid and massive internalization of the mesoderm, which contrasts with the much more modest movements of the ectoderm. In the Xenopus embryo, the differences in morphogenetic capabilities of ectoderm and mesoderm can be connected to the intrinsic motility of individual cells, very low for ectoderm, high for mesoderm. Surprisingly, we find that these seemingly deep differences can be accounted for simply by differences in Rho-kinases (Rock)-dependent actomyosin contractility. We show that Rock inhibition is sufficient to rapidly unleash motility in the ectoderm and confer it with mesoderm-like properties. In the mesoderm, this motility is dependent on two negative regulators of RhoA, the small GTPase Rnd1 and the RhoGAP Shirin/Dlc2/ArhGAP37. Both are absolutely essential for gastrulation. At the cellular and tissue level, the two regulators show overlapping yet distinct functions. They both contribute to decrease cortical tension and confer motility, but Shirin tends to increase tissue fluidity and stimulate dispersion, while Rnd1 tends to favor more compact collective migration. Thus, each is able to contribute to a specific property of the migratory behavior of the mesoderm. We propose that the "ectoderm to mesoderm transition" is a prototypic case of collective migration driven by a down-regulation of cellular tension, without the need for the complex changes traditionally associated with the epithelial-to-mesenchymal transition.