UPDATE 11th June 2020: The Call of Duty: Modern Warfare Season 4 download has gone live - and it's huge.
The download weighs in at 45GB on PC, 32.375GB on PS4, and 44GB on Xbox One. However, some Xbox One users are reporting having to download over 84GB with this morning's update. Activision has said it's investigating the issue.
Activision has said that once installed, the Series 4 update will only take up an additional 4GB on consoles.