The first piece of DLC is called, “The Signal” and according to a countdown which currently says 27 days, it should becoming out around June 1st. The description on the first episode states that it “answers many of the questions the end of the game raised,” including “what happened to the writer after the dramatic events of Season One?” This is the same DLC that all new purchasers of the game will receive with their game.
The second DLC, that is slated simply as “coming soon”. This DLC is called “The Writer,” and is described as “Wake struggling to not lose himself in the torrent of nightmares that assault him.” This seems to be a DLC that takes place mid story rather then at the end. The current price for the second DLC is unknown.