Christie made the decision based on calculations by the Federal Transit Administration and the New Jersey Transit.
"I have made a pledge to the people of New Jersey that on my watch I will not allow taxpayers to fund projects that run over budget with no clear way of how these costs will be paid for," Christie said. "Considering the unprecedented fiscal and economic climate our State is facing, it is completely unthinkable to borrow more money and leave taxpayers responsible for billions in cost overruns."
U.S. Transportation Secretary Ray LaHood has ordered a meeting with Christie for Friday.
The final budget is expected to top $11 billion and could exceed as much as $14 billion, compared to the project's current budget of $8.7 billion.
The federal commitment is capped at $3 billion and the federal government requires that any costs above $8.7 billion must be absorbed by the State of New Jersey. Cost overruns are estimated to be in a range from more than $2 billion to over $5 billion.
"While we recognize the importance and value of a cross-Hudson transportation improvement project, the current economic climate in New Jersey simply does not allow for this project to continue considering the substantial additional costs that are required," Jim Weinstein, executive director of NJ Transit, said.
The commuter tunnel has been planned for 20 years and is already under construction.
Officials have said the tunnel - dubbed Access to the Region's Core, or ARC - would create 6,000 construction jobs and add at least 40,000 new jobs after it is completed. If Christie were to divert money to the state transportation fund, that could also create jobs, depending on the projects.
Christie said staff will immediately begin a shutdown of the tunnel project.
Proponents of the tunnel, including leading state Democrats, assailed the Republican governor's decision as shortsighted and wrong-headed.
"This devastating blow will hurt our state and its economy for generations to come," said Assemblyman John Wisniewski, chairman of the state Democratic organization.
Wisniewski, who also leads the Assembly transportation panel, accused Christie's advisers of inflating the cost of building the tunnel.
Currently, NJ Transit and Amtrak share a two-track tunnel beneath the Hudson River. The project would add two more tracks. It would double the number of NJ Transit trains that could pass under the river.
More than 625,000 people trek into Manhattan from New Jersey each work day, but only 185,000 of them do so by rail. NJ Transit estimates the new tunnel would boost ridership.
During his campaign for governor last year, Christie supported the project.
But as soon as he announced the work stoppage, lawmakers and transportation officials suggested Christie had planned to scrap the project and to use the state's share of the money to pay for the nearly broke Transportation Trust Fund, which pays for local road projects and existing rail repairs.
Christie has refused to raise the state's gas tax, which is among the lowest in the country, to replenish the fund.
So far, about $600 million has been spent on the tunnel project. New Jersey could be on the hook to repay half of that to the federal government for breaking its commitment.
Sen. Frank Lautenberg says canceling the $8.7 billion tunnel violates an agreement with the feds.
Before the news conference, Christie spoke to Transportation Secretary Ray LaHood, whose spokeswoman indicated the project might not be dead. The spokeswoman, Olivia Alair, said in an e-mailed statement that LaHood and Christie plan to meet Friday afternoon to "discuss a path forward on the ARC tunnel project."