The movie will be released on 2019, and will be directed by Jeffren Katzenberg and Steven Spielberg with the help of animation professionals Pete Docter and John Lasseter. It will feature the returning voices of Mike Myers, Eddie Murphy, Cameron Diaz and Antonio Banderas, as well as the newcomers Jim Carrey as Mario, Dan Castellaneta as Wario, Chris Rock as Bowser, Angelina Jolie as Samus and Justin Bieber as Marth.
Dreamworks said that this is only the first of many works with Nintendo.
I will update when it gets new information.
UPDATE: Dreamworks released information on the story:
Quote: Dreamworks Animation
The beloved Shrek is in a all-new adventure in Nintendo's Super Smash Bros. world. A mysterious villain creates a magic portal that sends Shrek and Donkey to the Super Smash Bros. world, and they need to find a way to get back home. And they will encounter some beloved Nintendo characters to help and stop him. At the same time, Fionna and Puss in Boots need to find this mysterious villain before it's too late.
UPDATE: Dreaworks released the logo: