The first episode is coming out for computer platforms (no Linux yet though, but hopefully their Linux testing period yields results soon) and consoles (except for Wii U) on the 23rd of February, and the iOS and Android versions will be following, two days later, on the 25th.Beyond that, they've already announced the release months for episodes two and three. Episode two will be releasing in March, followed by episode three in April. Hopefully this is a sign that their future releases, from Batman and beyond, will be released on a similar schedule.
It turns out that the quick release schedule of Minecraft: Story Mode isn't a fluke after all. Their three episode Walking Dead: Michonne miniseries will be released on a monthly schedule.