Work on the $35.4 million expansion project was held up after another contractor filed a protest of the award to Turner Construction Co. But the U.S. Army Corps of Engineers reviewed the bid award and rejected the protest.
A notice to proceed was issued Friday.
The fourth building for the museum near Dayton will allow relocation of the Presidential Aircraft Gallery from a hangar in a restricted-access area of Wright-Patterson Air Force Base. A gallery on research and development will also move, and a new space gallery will showcase a space shuttle exhibit. Another gallery will focus on airlift operations.
The fourth building is now expected to open in 2016.