The MTA is set to unveil a plan to fix the city’s rotting subway signal system that would cost $37 billion — and take a decade of increased night and weekend closures to get done, transit sources told The Post Tuesday.

The proposal — which will address the biggest issue causing massive delays, faulty signals — would see $19 billion spent in the first five years, and another $18 billion in the next five, sources said.

Officially set to be revealed on Wednesday, the plan would require approval from the MTA board, the legislature and the governor.

This 10-year timetable to replace the troubled signal system is than the 40 years the had been previously been estimated if the work had been more spread out, according to the proposal, which was put forward by Andy Byford, head of New York City Transit.

Under the first five years of the plan, the agency hopes to replace dilapidated, decades-old signals on parts of the Lexington Avenue line, the A/C/E lines and the F and G lines, sources said.

These fixes will affect about 3 million riders.

The MTA will have to shut the lines and parts of lines down on weekends and nights more frequently than it does now to get the project done on time, said an agency source.

MTA Chairman Joe Lhota, however, disputed that, saying the shutdowns won’t be any more frequent than they are now.

The plan will also add more wheelchair accessibility to an additional 50 stations within the next five years, said a source. It will not however, pay to fix dilapidated subway stations.

Byford also plans to reorganize New York City Transit management to create more accountability down to the station level, the source said.

“We recognize that there are things in New York City Transit culture that needs to change,” the source said.

The plan will initially use the same communications-based train-control technology that is on the L train and being installed on the No. 7 line, but the agency also plans to add a more high-tech ultra-wideband, which uses a super-sensitive GPS system.

While sources put the cost of the plan at $37 billion, Lhota said “The costing of the Byford Plan is not complete. It will be completed in connection with the development of the 2020-2024 Capital Plan. Any estimates are premature and are inevitably inaccurate.”

Advocates say they are impressed with the scope of the plan but also want to know where the money is coming from. “The plan is the bold yet credible proposal to actually fix the subway that riders have been waiting for,” said Danny Pearlstein, a spokesman at Riders Alliance. “Now it’s time for Gov. Cuomo and the legislature to come up with a way to pay for it to get New Yorkers moving again.”