The third-largest city in the US had been battling for the site against San Francisco, California.
The selection of the Mid-west city was a surprise given Lucas' close ties with the state of California.
His home and visual effects company LucasFilm is based there. The museum is currently scheduled to open in 2018.
The news was confirmed by Chicago Mayor Rahm Emanuel's office on Tuesday, though no further details were offered.
Lucas has referred to Chicago as his "second home" in the past. His wife, Mellody Hobson, is from the city and they celebrated their wedding there.
The city has reportedly offered a patch of real estate along Lake Michigan near other popular attractions including the Field Museum of Natural History and the Shedd Aquarium.
San Francisco is said to have rejected Lucas' first choice of sites near the Golden Gate Bridge.
A vote by the museum's board to accept the decision is expected on Wednesday, the Chicago Tribune reports.
The board is also expected to change the museum's name from the Lucas Cultural Arts Museum to the Lucas Museum of Narrative Art.
Among the items said to be in the museum's collection are Norman Rockwell paintings and a scale model of the Millennium Falcon, the spacecraft helmed by Han Solo in the original film series.
Star Wars creator George Lucas has selected Chicago as the future site of a museum of his film memorabilia and prized art collection.