Eli Broad has finally ended the guessing game and declared his intention to build his museum in Downtown LA after the project received final approval today:

The 120,000-square-foot museum will cost $80 million to $100 million, Eli and Edythe Broad said today in an e-mailed statement. He will also pay $7.7 million to lease the land, and they will endow the Broad Art Foundation with $200 million to cover its ongoing annual operating expenses.

The project, to be designed by New York-based architects Diller Scofidio & Renfro, received final approval today from the Grand Avenue Authority, made up of city and county officials who oversee the areas’ redevelopment, said Broad, 77. Construction is set to begin in early 2011 and be completed in late 2012.

The new museum will provide a home for some of Broad’s 2,000 pieces of art, which he’s been collecting for more than three decades.

Eli Broad to Build Museum, Foundation Offices in L.A. (Bloomberg)