For nearly a quarter-century, governors and mayors in New York have been stymied in their attempts to fix Pennsylvania Station, one of the busiest transit halls in the Western Hemisphere and one of the most crowded and confusing.

Gov. Andrew M. Cuomo on Tuesday presented a fast-track plan that would finally create a train hall and retail space in the James A. Farley Building, also known as the General Post Office, on the west side of Eighth Avenue in Manhattan, while renovating the cramped, dingy underground passageways and platforms across the avenue at Penn Station.

The Farley Building would become a home for both Amtrak and, in a break with past proposals, the Long Island Rail Road; that should bring some relief to the congestion at Penn Station, which also houses New Jersey Transit trains and two subway lines. On any given day, more than 600,000 commuters and travelers — triple what the station was designed for — move through it.

The Farley train hall is expected to open in December 2020.

Mr. Cuomo, a Democrat, said his administration had selected a team — the developers Related Companies and Vornado Realty and Skanska AB, the giant construction management firm — for the $1.6 billion plan. He announced the plan at a luncheon for the Association for a Better New York, a business organization.