The show will feature the Royal Philharmonic Orchestra playing a live score while clips from the six films in the sci-fi franchise play on a cinema screen.
Lucas organised the project with composer John Williams. The musical will tour Europe following its British premiere in April.
"Star Wars holds memories for practically everyone," said AEG chief executive David Campbell.
"John Williams is the composer of our times, and fans will be thrilled to know that both he and Lucasfilm have contributed fully to this new production.
"To have the premiere at the O2 is a real coup for us, and I know there will be a lot of very happy Star Wars fans out there when they hear the news."
Tickets for the show go on sale on Monday.