The engines are assembled at Ford's Romeo engine plant on their niche-line. This is the same line and the same people that hand assembled the SVT Cobra and Lightning engines.
The Ford GT is "assembled and painted" at Saleen in Troy, MI. They basically do the initial assembly, putting together parts made by other suppliers. Mayflower builds the chassis and some of the body.
The final assembly is done at Ford's Wixom plant, where the engine and final interior pieces are installed.
For a more in depth explanation of the GT assembly,
Click Here. This should clear a few things up.
I am surprised no one has mentioned where the Viper Competition Coupes are built/assembled. The automotive world is a small one.