The spire will top the 104-story building, which will be 1,776 feet tall when it is completed, the New York Daily News reported.
The ceremony was scheduled for Monday but was delayed by bad weather.
For many of those watching below as a crane raised the flag-draped spire, the moment marked the beginning of the end of something that began on Sept. 11, 2001, when the twin towers of the World Trade Center collapsed after being hit by hijacked planes. Steven Plate, the director of construction, called it "putting the candle on the cake."
Thomas Barrows, a construction worker, watched intently.
"You put your heart, your sweat, your blood to the project," Barrows said. "Seeing the American flag, my eye gets teary. It's very joyful for our country. It means a lot. New York needs it. America needs it."
The spire weighs about 758 tons, NBC News reported.
The new One World Trade Center is on the site of Six World Trade Center, a six-story building that collapsed several hours after its taller neighbors.
Once the building's height is verified, the tower will be the tallest structure in the Western Hemisphere and the third tallest in the world, NBC News said.
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