In a statement issued Wednesday, Cuomo said "formal construction" began with the driving of piles that will be part of the bridge's foundation.
For months, the site in the Hudson River has been busy with pre-construction activity. That includes dredging and building platforms.
The bridge is to replace the aging span that now connects Westchester and Rockland County. It's expected to cost $3.9 billion.
Funding is not yet in place. The state is hoping that a federal loan will help limit the expected large hike in the current $5 toll.
Cuomo said some traffic should be on the new bridge by late 2016 and the entire project should be done by 2018.
