Mehdorn, 70, takes over the helm of FBB, a consortium which includes the German state and city of Berlin, in charge of building Berlin-Brandenburg Airport, originally slated to have opened in June 2012.
Transport Minister Peter Ramsauer said Mehdorn's appointment marked "an important step" in putting FBB on the "path to success."
The new airport will replace Berlin's two existing airports, Tegel in the west of the city, and the southeastern-located Schönefeld, on the latter's current site.
But its opening has been postponed indefinitely after several previous delays due to a series of technical issues, raising concerns that it has tarnished Germany's legendary image for efficiency.
While he was head of Germany's second-largest airline Air Berlin, Mehdorn was highly critical of the delays dogging the opening of the new airport and Air Berlin filed a legal complaint.