The download size has been listed for the digital version of Dark Souls 2: Scholar of the First Sin on Xbox One. The official Xbox Store revealed that the remastered release is going to take up 12.2 GB on the HDD of the system. Of course, the disc release is also available for preorder with this page on Amazon if you have any concerns about using up your internet bandwidth.
In comparison, Dark Souls 2 took 5.75 GB to download on the Xbox Live Marketplace of the Xbox 360. The huge disparity in size is due to all three major DLC packs (Crown of the Sunken King, Crown of the Old Iron King and Crown of the Ivory King) being included in Scholar of the First Sin) along with some next-gen exclusive features such as increasing the maximum amount of online players from four to six.
The Xbox One does come with a 500 HDD installed. You can add more space by using a compatible external hard drive or by installing an internal one using the Collective Minds 2.5-Inch Hard Drive Enclosure (you can purchase that accessory here).
Dark Souls 2: Scholar of the First Sin is coming out on the Xbox One on April 7.