The Port Authority of New York and New Jersey voted on Thursday to spend tens of billions of dollars on transforming La Guardia Airport, enhancing Newark Liberty International Airport and building a new central bus terminal in Midtown Manhattan.

“What you witnessed today is the most important board meeting in Port Authority history,” said Patrick J. Foye, the authority’s executive director. Mr. Foye said he thought it represented “the single largest allocation of capital” by the authority in one day.

While the agency’s capital spending plan already included major projects at La Guardia and Newark, it did not factor in a new bus terminal. So the decision to finance a new terminal before a final cost had been determined or before a plan or location for the facility had been approved came as something of a surprise.

It reflected the friction and divided priorities to which the authority’s bistate structure can lead — something captured in heated exchanges between John J. Degnan, the chairman of the board, appointed by Gov. Chris Christie of New Jersey, a Republican, and Mr. Foye, appointed by Gov. Andrew M. Cuomo of New York, a Democrat.