What structure catalyzes the formation of ATP during chemiosmosis?

The formation of ATP is controlled by the cytochrome oxidase (please check on the name!) of the electron transport chain in the mitochondria.. as H+ ions flow out along their concentration gradient, the release of this energy is coupled to the phosphorylation of ADP to form ATP.

You are asking about the structures called ATP synthases.  These are protein complexes embedded in the inner mitochondrial membrane, and are activated by protons "pumped" across this membrane during the passage of electrons down electron transport chains embedded in the same membrane.  A high proton concentration gradient is produced that promotes passage of protons back across the inner mitochondrial membrane, but they can cross the membrane only by passing through the ATP synthase complexes.  The ATP synthase has a rotary component and a stationary component; when activated the ATP synthase carries out what is usually referred to as oxidative phosphorylation of ADP to ATP.  It is referred to as oxidative because oxygen is required for the functioning of the electron transport chains; in the absence of oxygen the proton concentration gradient cannot be maintained between the two mitochondrial membranes and ATP cannot be synthesized.