Polarized cell shape changes during tissue morphogenesis arise by controlling the subcellular distribution of myosin II. For instance, during Drosophila melanogaster gastrulation, apical constriction and cell intercalation are mediated by medial-apical myosin II pulses that power deformations, and polarized accumulation of myosin II that stabilizes these deformations. It remains unclear how tissue-specific factors control different patterns of myosin II activation and the ratchet-like myosin II dynamics. Here we report the function of a common pathway comprising the heterotrimeric G proteins Gα12/13, Gβ13F and Gγ1 in activating and polarizing myosin II during Drosophila gastrulation. Gα12/13 and the Gβ13F/γ1 complex constitute distinct signalling modules, which regulate myosin II dynamics medial-apically and/or junctionally in a tissue-dependent manner. We identify a ubiquitously expressed GPCR called Smog required for cell intercalation and apical constriction. Smog functions with other GPCRs to quantitatively control G proteins, resulting in stepwise activation of myosin II and irreversible cell shape changes. We propose that GPCR and G proteins constitute a general pathway for controlling actomyosin contractility in epithelia and that the activity of this pathway is polarized by tissue-specific regulators.