Barnard Construction Co. of Pompton Plains and Judlau Contracting of New York will be paid $583 million to dig the mile-long tube.
Gov. Jon Corzine called the project "an engine for growth" that will create thousands of jobs.
However, several speakers at the meeting said the project is too costly and will require a gas tax or bridge and tunnel toll hikes.
The project is known as Access to the Region's Core, or ARC.
It's expected it will double train capacity into and out of Manhattan by adding two single-track tunnels under the Hudson River.
Final engineering and design work will also begin on a pair of new bridges over the Hackensack River that will increase capacity, flexibility and reliability for rail customers traveling into and out of New York.
The board approved a contract amendment to advance construction of the Portal Bridge Capacity Enhancement project, a crucial link between Kearny and Secaucus on the Northeast Corridor that will replace the 99-year-old Portal Bridge.
"This project will provide an essential upgrade to our core capacity and positions NJ TRANSIT to efficiently accommodate growing ridership for decades to come," said NJ TRANSIT Chairman and Transportation Commissioner Stephen Dilts.
The new bridges will offer five tracks - three more than the current bridge - providing the capacity to take full advantage of the additional capacity into and out of New York that the Mass Transit Tunnel project will create. The complementary bridge and tunnel projects will eliminate two bottlenecks for NJ TRANSIT and Amtrak customers.
In addition, the new fixed bridges will provide greater reliability by eliminating the need for a movable span. The new bridges will be built high enough above the river - 50 feet above mean high water - to allow ships to pass underneath with none of the bridge opening and closing operations that create delays for rail customers.
"The current bridge is functionally obsolete and expensive to maintain," said NJ TRANSIT Executive Director Richard Sarles. "This project will eliminate a chokepoint for hundreds of trains and thousands of customers each day."
Preliminary construction is expected to start by mid 2010, with some heavy project construction including access roads, platforms and piers to start in the fall.
The entire project, estimated to cost about $1.7 billion, is expected to be completed in 2017. A combination of state and federal sources is expected to provide funding.
Finally, Jersey shore residents will soon be able to ride a bus to Newark Liberty International Airport.
The board approved a $10 million contract for Academy Lines to operate the route.
The No. 60 buses will leave the Toms River Bus Terminal and stop at several park-and-ride lots along the Garden State Parkway.
When they reach the airport, the buses will stop at the South Area; Terminals A, B, and C; and the North Area Transit Center.
The bus service will begin New Year's Day as part of a 30-month trial.
