The spire makes the building the tallest building in the Western Hemisphere, 47 feet taller than Chicago's Willis Tower, though it is substantially shorter than towers in the Middle East and Asia.
"I am very happy, but also sad, because why did we have to rebuild this tower? It's a proud day for the city," said Philip English, one of a couple dozen construction workers on hand as the spire was completed at 7:46 a.m. local time (1146 GMT).
The skies were crystal clear, reminiscent of the weather on the day that hijacked airliners crashed into the former Twin Towers, in a coordinated attack on New York and Washington that killed about 3,000 people and left the United States on high alert for future incidents.
Formerly called the Freedom Tower, One World Trade Center is one of four skyscrapers being built around the site of the fallen Twin Towers in a partnership between developer Larry Silverstein and the Port Authority of New York and New Jersey, which owns the site.
The tower's height is a reference to the year 1776, which marked the beginning of the American revolution against British rule and is considered the start of what became the modern United States.
(Reporting by Elly Park; Writing by Scott Malone)