Via Ign.com:
Star Wars: Episode IX will be directed by Jurassic World director Colin Trevorrow. Recently it was confirmed JJ Abrams — who’s heading up The Force Awakens — would not direct Episode 9. It was also confirmed that Trevorrow would not direct Jurassic World 2.

Lucasfilm’s Kathleen Kennedy said in a statement, “Colin is someone I’ve been interested in working with ever since I saw Safety Not Guaranteed. The power of that film paired with the enormous success of Jurassic World speaks volumes about his abilities both as a storyteller and skilled filmmaker. We are thrilled to have such an incredible talent as Colin join our family and step into the Star Wars universe.”

Trevorrow added, “This is not a job or an assignment. It is a seat at a campfire, surrounded by an extraordinary group of storytellers, filmmakers, artists and craftspeople. We’ve been charged with telling new stories for a younger generation because they deserve what we all had—a mythology to call their own. We will do this by channeling something George Lucas instilled in all of us: boundless creativity, pure invention and hope.”
Production for Episode 9 will not begin for “a few years.”