Respiratory chain complexes assemble into functional quaternary structures called supercomplexes (RCS) within the folds of the inner mitochondrial membrane, or cristae. Here, we investigate the relationship between respiratory function and mitochondrial ultrastructure and provide evidence that cristae shape determines the assembly and stability of RCS and hence mitochondrial respiratory efficiency. Genetic and apoptotic manipulations of cristae structure affect assembly and activity of RCS in vitro and in vivo, independently of changes to mitochondrial protein synthesis or apoptotic outer mitochondrial membrane permeabilization. We demonstrate that, accordingly, the efficiency of mitochondria-dependent cell growth depends on cristae shape. Thus, RCS assembly emerges as a link between membrane morphology and function.