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.

“This plan is smarter and better for people who will use the complex,” Mr. Cuomo said in an interview. “And it will actually happen.”

According to state officials, all of the necessary approvals are in place, as well as the funding. The developers would pay New York State about $600 million, which would include an upfront payment of $230 million and annual payments in lieu of taxes over 30 years, which the city has to approve. The developers would also provide the state an unspecified share of the retail revenues at the train hall and, possibly, advertising, officials said.

Empire State Development, a state agency, would contribute $570 million toward the remaining cost, much of it coming from the probable sale of Farley’s air rights. Amtrak, which owns Penn Station; the Long Island Rail Road; the Port Authority of New York and New Jersey; and the federal government would put in a combined $425 million.

Senator Daniel Patrick Moynihan, who died in 2003, originally championed the idea of creating an adjunct train depot at the Farley Building in an effort to restore grandeur to Penn Station, where the aboveground train hall was torn down in the 1960s to make way for Madison Square Garden.

Both Farley and the demolished train hall were designed by architects at McKim Mead & White.

Plans to convert the post office into a train station have been derailed by disputes involving the Postal Service and Amtrak, a lack of funding and the difficulty of doing construction work without disrupting train service.

In 2005, the state selected Related and Vornado to do the work, a $900 million project. The developers initially sought to move Madison Square Garden to the west side of the post office building so that they could build skyscrapers or a glass-encased mall over the Penn Station site. But the project never really moved forward.

Last January, Mr. Cuomo abruptly announced that he was starting over and requested proposals for both the post office building and Penn Station, although the original developers had a major head start over any rivals. Senator Chuck Schumer, Democrat of New York and a longtime supporter of the project who has obtained federal money for preliminary work, called the governor’s announcement a “step forward in the modernization of our West Side transportation network.”

Mr. Cuomo said his new plan fixed flaws in previous proposals. Moving both Amtrak and Long Island Rail Road passengers to Farley would do a lot more to relieve congestion at Penn Station, he said.

Jeff Blau, chief executive of Related Companies, who had been taken aback by the Mr. Cuomo’s announcement in January, was excited about finally moving forward.

Related, Vornado and Skanska are expected to sign a formal contract early next year that would include a timetable with financial penalties if deadlines are not met.

At the Farley Building, the developers would create a massive train hall beneath a one-acre glass skylight mounted on the building’s dramatic steel trusses for the daily 30,000 Amtrak riders and 230,000 Long Island Rail Road passengers.

Tom Wright, president of the Regional Plan Association, a private planning group that has long favored the Farley project, said the announcement on Tuesday was a major advance.

“The vision for the full complex,” Mr. Wright said, “has got to be a seamless, integrated system. Whether someone’s riding Amtrak, the subways or the L.I.R.R., they should be able to enter the complex and get to their platform as quickly as possible.”

State officials said they would begin soliciting bids on Tuesday for work at Penn Station.

Correction: September 30, 2016

An article on Wednesday about Gov. Andrew M. Cuomo’s fast-track plan to create a train hall and retail space in the James A. Farley Building while renovating Pennsylvania Station misstated part of the name of the architecture firm that designed the Farley Building and the now-demolished train hall at Penn Station. It is McKim Mead & White (not Wright).

Correction: October 2, 2016 
An earlier version of a picture caption with this article carried an incorrect credit. The rendering of a new station at the James A. Farley Post Office is by SOM/VOLLEY, not SOAM/VOLLEY.