Federal and state officials announced an agreement on Wednesday to create a corporation within the Port Authority of New York and New Jersey to oversee long-awaited plans to build a new rail tunnel under the Hudson River.

The entity, called the Gateway Development Corporation, will coordinate the project and assemble the billions of dollars needed to pay for it. It will be controlled by a four-member board with representatives from New York, New Jersey, Amtrak and the federal Transportation Department.

As part of the agreement, the federal government and Amtrak said they would be responsible for financing half of the project, which could cost as much as $20 billion. Govs. Chris Christie of New Jersey, a Republican, and Andrew M. Cuomo of New York, a Democrat, had pushed for the cost-splitting and said the two states would line up the money for the other half.

The announcement, from the governors and Senators Chuck Schumer of New York and Cory A. Booker of New Jersey, both Democrats, signaled the most significant progress yet on an effort federal officials have called one of the most important infrastructure proposals in the country. The century-old rail tunnel used by Amtrak and New Jersey Transit that runs under the river is deteriorating and needs repairs because of damage by Hurricane Sandy.