The 72-year-old moviemaker had initially intended to open his new museum, which is to be known as the Lucas Museum of Narrative Art, in Chicago - but was forced to change his plans after running into legal challenges from an open-spaces group.
Los Angeles mayor Eric Garcetti welcomed the museum's impending construction in the city, saying in a statement: "I believed in the vision for the Lucas Museum, and we went after it with everything we have - because I know that LA is the ideal place for making sure that it touches the widest possible audience.
"I am deeply grateful to [Lucas' wife] Mellody and George, and to our educational, governmental, and cultural leaders for their extraordinary support in helping us bring the museum home. Now it's time to build the vision."
The venue will feature paintings, illustrations and digital art from the 'Star Wars' franchise, which George sold to Disney in 2012.
The proposed site for the museum is the next to the University of Southern California, which is where George studied in his youth and where he also met award-winning director Steven Spielberg.
Following Disney's acquisition of the 'Star Wars' franchise, it was widely expected that George would have a significant involvement in the new movies.
However, he has since admitted that his vision for the series and those of Disney failed to chime.
He shared: "The issue was, ultimately, they looked at the stories and they said, 'We want to make something for the fans.' People don't actually realise it's actually a soap opera and it's all about family problems - it's not about spaceships.
"So they decided they didn't want to use those stories, they decided they were going to do their own thing so I decided, 'Fine ... I'll go my way, and I let them go their way.'"