Gov. Andrew Cuomo, son of the bridge's namesake, says four lanes of Rockland-bound traffic will start crossing the first span of the bridge late Friday night into Saturday morning.
Workers will begin shifting the lanes onto the new bridge at 9 p.m.
The second span is slated to open next year.
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The Democratic governor introduced a new $4 billion bridge Thursday with a ribbon-cutting ceremony.
He said it was worth the cost and the wait.
"This bridge will handle more traffic, it will move it faster on more lanes, it's more technologically advanced, cashless tolling, state of the art security measures, bike and pedestrian access, bus and rail ready," said Cuomo.
The project launched by the Thruway Authority in 2013 will replace the 62-year-old Tappan Zee Bridge, a critical link in the Northeast U.S. highway system.
The Tappan Zee had served as the poster child for crumbling infrastructure. President Barack Obama used it as a backdrop in 2014 when he asked Congress for more infrastructure funding.
The first span of the long-awaited replacement is expected to carry more than 50 million cars across the Hudson River.
The 62-year-old structure has served as the poster child for America's crumbling infrastructure, and the second span is scheduled for completion in the spring.
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The 3-mile bridge linking Westchester County to the New York State Thruway across the widest point in the Hudson is one of the largest public infrastructure projects underway in the U.S. and a model of the latest engineering.
The construction project, begun by the Thruway Authority in 2013 after decades of political squabbling, still rankles upstate critics who want to know exactly how the state is paying for it.
"Repeatedly we've heard whispers about raising tolls across the Thruway system to pay for a bridge many upstate commuters will never use," said Greg Biryla, executive director of Unshackle Upstate, a coalition of business and trade organizations. "The Thruway is the economic lifeline between our communities. When you increase the cost of that lifeline, you do further damage to the struggling upstate economy."
(The Associated Press contributed to this report)