To be clear, the studio he has created (Kojima Productions) is independent. It's just the game that is exclusive.
No information about the new game was released, but that isn't surprising. The reality is that Kojima's next game is likely a few years away from an official reveal, even farther away till a release. Still, the news is exciting and finally ends a long series of strange events.
Kojima has been the center of a bizarre gaming story for the last year now. From rumors he had been fired, to rumors that he was on vacation, to the removal of his name from game boxes and recently the fact he was legally barred by Konami from attending The Game Awards 2015. The last year has sounded like a mess for Kojima and the many people who worked at his studios.
Hopefully some of the men and women who worked with Kojima on games like Metal Gear Solid V will find employment at Kojima's new studio, which is called Kojima Productions. It also has a cool logo. Speaking of cool stuff, check out Kojima's new beard. I like it.
There isn't any more information about the game, the partnership with Sony or if that sweet new beard is permanent. Let the speculation begin. And while you do speculate, check out the Kojima Productions website which is as weird as you probably expected.