New Jersey will borrow $600 million, double the amount it initially intended, to jump-start the replacement of a century-old rail bridge that causes delays on the nation’s busiest passenger rail line.

Earlier this year, Transportation Secretary Elaine Chao challenged New York and New Jersey to put more “skin in the game” to pay for the Gateway program, which includes the replacement of the Portal Bridge at Kearny, N.J.

A...