According toit's "a special thanks" to fans who've been playing the near-future shooter in its earliest weeks, and you'll only be able to earn it until December 1.
To get the full kit, and as you can see it's a snazzy one, you'll still have to earn 'supply drops', Advanced Warfare's version of loot. Supply crates tend to drop every half hour or so, but it's unclear exactly what the drop rate for the limited edition costume is. Might take some time, is what I'm saying.
The game will notify you of the new content as soon as you log in, then it's up to you to track it down. Good hunting.