In a joint announcement, New York Gov. Andrew Cuomo and New Jersey Gov. Chris Christie said the service would return between Hoboken and 33rd Street in Manhattan, beginning Wednesday morning, The New York Times said.
The Port Authority of New York and New Jersey said direct service between Hoboken and the World Trade Center still was "several weeks away" because of work to replace damaged and destroyed signal equipment.
Most subway, bus and transit operations in New York and New Jersey resumed soon after Sandy made landfall, but the PATH train in Hoboken was considered the missing link in the region's transportation system, the Times said.
The Port Authority said more than 10 million gallons of water was pumped from tunnels and workers replaced much of the train system's switching and signaling equipment.
Without PATH service, many Hoboken residents lined up for ferries and buses, often doubling their commute time, or bore the expense of a daily taxi ride, the Times said. Because fewer visitors were able to get to Hoboken, business owners reported sales decreases of 25 percent to 70 percent since the storm.