We first caught wind that Square Enix was releasing a World of Final Fantasy mobile game back in November and now, as promised, it's available in Japan.
In World of Final Fantasy: Meli Melo, you've got to collect, raise, and summon beasts of the world and battle your opponents to your heart's content. Though this is an all-new story, keep your eyes open for familiar characters to appear.
As we previously noted, this game is a casual combat game, and from what I can gather from its description it focuses heavily on collecting the 100+ monsters and using magical stones to evolve them in the way you want.
It also looks like the game continues to run on its own, collecting items and caring for your monsters even when you're not in the application.
Though the game is free to play on the Japanese App Store, the base of its description covers the details of its subscription service, so do give those a quick read if you want to give the game a go.