How does the matter that makes up the fat of your fat cells ultimately leave your body--following weight loss?
Yes, they are mostly exhaled. The carbon, hydrogen and oxygen that the fats are made of recombine to become $CO_2$ and $H_2 O$ and are exhaled. 

It's the same overall chemical reaction as if the fats / carbohydrates were burnt, except it's by a different pathway, and the energy produced goes (mostly) towards driving other chemical reactions rather than becoming light and heat.