The physics of star formation and the deposition of mass, momentum and energy into the interstellar medium by massive stars ('feedback') are the main uncertainties in modern cosmological simulations of galaxy formation and evolution(1,2). These processes determine the properties of galaxies(3,4) but are poorly understood on the scale of individual giant molecular clouds (less than 100 parsecs)(5,6), which are resolved in modern galaxy formation simulations(7,8). The key question is why the timescale for depleting molecular gas through star formation in galaxies (about 2 billion years)(9,10) exceeds the cloud dynamical timescale by two orders of magnitude(11). Either most of a cloud's mass is converted into stars over many dynamical times(12) or only a small fraction turns into stars before the cloud is dispersed on a dynamical timescale(13,14). Here we report high-angular-resolution observations of the nearby flocculent spiral galaxy NGC 300. We find that the molecular gas and high-mass star formation on the scale of giant molecular clouds are spatially decorrelated, in contrast to their tight correlation on galactic scales(5). We demonstrate that this decorrelation implies rapid evolutionary cycling between clouds, star formation and feedback. We apply a statistical method(15,16) to quantify the evolutionary timeline and find that star formation is regulated by efficient stellar feedback, which drives cloud dispersal on short timescales (around 1.5 million years). The rapid feedback arises from radiation and stellar winds, before supernova explosions can occur. This feedback limits cloud lifetimes to about one dynamical timescale (about 10 million years), with integrated star formation efficiencies of only 2 to 3 per cent. Our findings reveal that galaxies consist of building blocks undergoing vigorous, feedback-driven life cycles that vary with the galactic environment and collectively define how galaxies form stars.