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. Display omitted •Dissociation of cristae remodeling from OMM permeabilization•Cristae shape determines assembly of respiratory chain supercomplexes•Efficiency of mitochondrial respiration and cellular growth depends on cristae shape The ability to perturb cristae shape without affecting other key aspects of mitochondrial physiology reveals that membrane shape influences supercomplex assembly and stability to regulate mitochondrial respiration and cellular respiratory growth. Quaternary structures such as supercomplexes therefore emerge as a link between membrane morphology and function.