The Port Authority Thursday chose LaGuardia Gateway Partners, a consortium that includes construction and banking firms, to replace an aging terminal at LaGuardia Airport, ending months of delay.

The $3.6 billion project calls for the demolition of the 51-year-old Central Terminal Building, known to travelers as Terminal B, and the construction of a new and larger one that would accommodate more than twice as many passengers.

The authority's board also said it would consider spending up to $400 million more, bringing the total cost to $4 billion, to build a connection at the Queens airport between the new Terminal B and Terminal C, an element recently added to the project by an outside panel overseeing Gov. Andrew M. Cuomo's airport design competition.

"Today, we are taking a major step toward the renovation of LaGuardia Airport . . . ," John J. Degnan, chairman of the authority's 11-member board, said Thursday in Manhattan.

The Port Authority, which operates LaGuardia, Kennedy and Newark Liberty International airports, selected LaGuardia Gateway Partners -- a group that included Skanska, Walsh Construction, Morgan Stanley and Citigroup -- over LGA Central Terminal Consortium.

The Port Authority will pay $1.1 billion to improve the infrastructure while LaGuardia Gateway Partners will pay the remaining $2.5 billion to design, build and operate the terminal under a 35-year lease to be negotiated.

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The proposal includes a new 35-gate terminal with more restaurants, shops and larger areas for passenger and baggage screening. The completion date for the project was initially set for 2021, but that date has been pushed back.

LaGuardia consistently ranked among the worst U.S. airports in cleanliness, design and delays. Last year, Vice President Joe Biden derided it as an airport that could be found in "some Third World country."

In August 2013, the bi-state authority asked interested parties to submit proposals. In May 2014, it received plans from three groups. The authority's board was expected to select a winning team last fall, but the decision was put off after Cuomo announced an airport design competition in October, prompting business and transportation groups to criticize the delays.

Thursday, they took a different stance and praised the board for finally choosing a team and moving the project along.

"A new terminal is the linchpin in finally changing LaGuardia's reputation from Third World to world class . . . ," said board members of Global Gateway Alliance, which advocates for improvements to the region's airports.