Activision has explained that if you have Modern Warfare 2 installed and up to date, you should already have Warzone 2.0 preloaded. If you don't own Modern Warfare 2, you'll have to download all 23GB of Warzone 2.0 seperately.

PSA: Warzone 2.0 (If you've purchased Modern Warfare II, you'll already have Warzone 2.0 preloaded)