Kennedy is also positioned to run the studio once Lucas retires.
Earlier this year, Lucas revealed he is retiring from making films, saying that he is "moving away from the business, from the company, from all this kind of stuff".
He expressed the same sentiment in a recent interview with Empire magazine.
"I'm moving away from all my businesses, I'm finishing all my obligations and I'm going to retire to my garage with my saw and hammer and build hobby movies," Lucas said.
Kennedy, a seven-time Academy Award nominee, is a longtime collaborator with Lucas's close friend Steven Spielberg. Her producing credits vary from the big franchises Jurassic Park, Indiana Jones and Bourne to period pieces like Spielberg's War Horse and the new Lincoln biopic.
"I've spent my life building Lucasfilm and as I shift my focus into other directions I wanted to make sure it was in the hands of someone equipped to carry my vision into the future," Lucas said in a statement.
"It was important that my successor not only be someone with great creative passion and proven leadership abilities, but also someone who loves movies."
Spielberg also said: "Kathy has been a member of both of our families going into a fourth decade so it does not feel like she is going to another galaxy far far away. She will get just as much support from me with Lucasfilm as George has given both of us all these years."
Watch the trailer for War Horse below: