By Hilary Russ

NEW YORK (Reuters) - The government corporation charged with overseeing Amtrak's $24 billion Gateway rail project between New York and New Jersey has filled out its governing board, sources told Reuters on Wednesday.

The Gateway project, one of the most important and urgent rail projects in the United States, calls for the construction of a new train tunnel and the repair of the existing, century-old between the two states, which officials have said could become unusable within the next decade.

Closing of the tunnel would affect tens of thousands of NJ Transit rail commuters and Amtrak's Northeast Corridor route between Washington and Boston, the railroad's most important line.

U.S. Transportation Secretary Anthony Foxx and Amtrak board Chairman Anthony Coscia will serve on the newly established oversight body, called the Gateway Program Development Corporation, according to two sources with direct knowledge of the situation.

The corporation will also include two Port Authority of New York and New Jersey board members: Vice Chairman Steven Cohen, nominated to the Port Authority by New York Governor Andrew Cuomo, and Richard Bagger, selected for the authority by New Jersey Governor Chris Christie, the source said.

The Port Authority officially approved the formation of the corporation earlier this month. It is being led by director John Porcari, an executive at consulting firm Parsons Brinckerhoff.

On Tuesday, President-elect Donald Trump said he plans to nominate former Labor Secretary Elaine Chao to head the Transportation Department as he develops his push for $1 trillion in new infrastructure spending to fix U.S. roads, airports, water systems and bridges.

Proponents of the Gateway project have questioned whether support would continue under a Trump administration.

Another source, who did not want to go on the record because the situation was still developing, told Reuters the Trump administration is expected to replace Foxx, a Barack Obama appointee, on the board after it takes office in January.

Loss of the tunnel would make commuting between New York and New Jersey a nightmare and potentially hurt the regional economy, which generates 10 percent of the national gross domestic product.

(Editing by Daniel Bases and Steve Orlofsky)