The $4 billion project is expected to be completed sometime in 2016.
Steven Plate, the head of World Trade Center construction for the Port Authority, said more than 700 5-feet-by-10 feet panels are being installed over the next several months.
It took nearly 45 minutes for workers to lift the first section to the rooftop of the 104-story building Wednesday morning.
The spire is divided into 18 sections, weighing between 5 tons and more than 67 tons. Workers will begin hoisting them on Wednesday.