The New York Metropolitan Transportation Council voted unanimously to approve the project.
The county executives from Westchester, Rockland and Putnam, who all sit on the board, said last week that they would vote for the project. They did not attend Monday's meeting but sent representatives who cast votes in favor of the project.
Each of the three in effect held veto power because the council must unanimously approve a project to qualify it for federal funds.
Following the vote, Gov. Andrew Cuomo signed a letter of intent to U.S. Secretary of Transportation Ray LaHood to formally apply for the funds to build a new bridge.
"We have done more in the last couple of months than we have in the past 13 years," Cuomo said of the plan's progress. "We have asked the federal government to expedite our application. We are going to Washington to apply."
When asked whether he believed the federal funding would be granted, Cuomo said: "They are going to say yes. You gotta believe, they are going to say yes."
Cuomo had garnered support from other officials but the three county executives - Rob Astorino of Westchester; Scott Vanderhoef of Rockland and MaryEllen Odell of Putnam - had expressed some doubts about the new bridge, principally over its lack of a full-scale mass transit component.
Under the current plan, the bridge would have a dedicated bus lane during rush hours but ambitious plans for a commuter rail line or bus mass transit were dropped because of high costs.
Howard Glaser, director of state operations, called the vote "an important step forward."
"There's been 10 years of study, hundreds of public meetings, and finally we'll begin to move forward," Glaser said. "The bridge is outdated, it's unsafe. Residents of Westchester and Rockland and Putnam deserve better, and it's an important economic lifeline for all of New York State."
The existing bridge, spanning the Hudson River between Westchester and Rockland counties, is overcrowded and deteriorating after more than 55 years of use.
The environmental group Riverkeeper on Friday criticized officials for giving only three days' notice for the vote on the new bridge.
In a statement Monday, Riverkeeper called the vote "a major departure from past promises of transparency and inclusiveness."
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Associated Press Writer Fay Abuelgasim contributed to this report.
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