A post on Battle.net outlines the tiered roll out of this new content. Hearthstone players located in the Americas will receive the Military Quarter on Wednesday, August 6 at 3 a.m. ET, while those in Europe will discover the Military Quarter on August 5 at 12 a.m. CEST. Taiwan and China will likewise receive the Military Quarter on August 5, at 12 a.m. CST, but Korea will be waiting until August 6 at 1 a.m. KST to receive the DLC. Unlike the Plague Quarter, which was offered to all players at no charge, the Military Quarter will bear a $7 (or 700 gold) price tag, though it can be purchased at a discount if you purchase the full complement of Naxxramas additions at $25.
Blizzard has yet to reveal the new bosses and cards included in the Military Quarter, but claims that an announcement should be appearing on the game's official website soon.
Edit: Originally this post stated that the Military Quarter is the second wing of Naxxramas, when it is actually the third released to date.