"Unfortunately, time has run out and the moment we've consistently warned about has arrived - Chicago's loss will be another city's gain," Emanuel said.
The city's official tourism organization, Choose Chicago, called it an "enormous loss."
The 17-acre site just south of the Chicago Bears' home stadium would have erased a parking lot and added 4.5 acres of new parkland, according to designs released in September. Supporters defended it as an improvement that would have transformed an asphalt expanse into green space with dazzling landscape design by renowned Chicago architect Jeanne Gang.
They said the museum's futuristic building " a sloping dune-like form topped with an observation deck resembling a floating disc "would have added to Chicago's tradition of bold architecture.
Friends of the Parks, which is committed to preserving open space, fought the location out of concern it would open the way for more construction on the valuable ribbon of public, open land along the Lake Michigan shoreline.
In a federal lawsuit, it said the city had no authority to hand over the land, citing a legal principle known as the public trust doctrine, which requires the state to ensure open spaces are preserved and accessible to the public.
Before Lucas had settled on Chicago, where his wife is from, he had considered locating the museum in San Francisco.
The museum, wherever it ends up, will showcase popular art Lucas has collected since college, including illustrations by Norman Rockwell, Maxfield Parrish and N.C. Wyeth, as well as works by Lucas's visual effects company, Industrial Light and Magic.
It will also feature digital media arts and film industry art, including props, costumes, set pieces and story boards. Museum officials say the vision is to highlight art that tells a story.