Construction on the facility in Washington Heights began in 2014 and was expected to take one year.
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The new concourse will be air conditioned, seat 125 people and include a gym, food outlets and stores.
The facility also has new technology, and improved signage, lighting and electronic communications.
For the first time since 2014, passengers will be able to access the facility at Fort Washington Avenue and take the escalator, stairs or elevator to the bus pavilion. There also are elevators at the Broadway entrance.
The tunnel connection between the station and the "A" subway station at 175th Street will not reopen Tuesday but eventually will. Commuters must use the stairs on 177th Street and Fort Washington Avenue.
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The station opened in 1963 and serves 5 million people annually.
The project, which was supposed to take a year, was directed by GWBBS Development Venture, on behalf of the Port Authority. It was the biggest renovation project for the bus station in five decades.
It also ran $17 million over budget, which was originally estimated at $183 million.
Commuters have been using a trailer on Fort Washington Avenue and 179th Street to serve as an interim location for bus station services.