Basically, the team at Kojima Productions had the "cut everything" technology down but couldn't design an interesting game around it. Because of this, the project was cancelled in 2010. Kojima then decided to look for a studio to help pick up the pieces. He first considered some Western studios, but decided that a Japanese studio would be a better fit for a ninja action game with sword combat. He ultimately came to the conclusion that PlatinumGames was the only studio that could pull it off. He contacted them earlier this year and they accepted. They originally planned to use the FOX engine and a story set between Metal Gear Solid 2 and Metal Gear Solid 4, but in order to give Platinum as much freedom as possible, they moved to Platinum's proprietary engine and a story set after Metal Gear Solid 4. Both studios seem happy about the collaboration.
I'm very curious to see who the director is, since Kojima said that the lack of a strong director was one of the main problems with Rising's original development process.