BART General Manager Dorothy Dugger said the vote is "one of the final steps" in getting the project, which has been discussed for more than 20 years, underway soon.
Dugger said, "This is a clear signal to the contracting committee that the region is serious about this project."
She said the transit agency has already started the bidding process for the project and bids are due in September.
BART directors are scheduled to award the contract in November and work will begin early next year if all goes well, Dugger said.
Work is expected to take three years and it's anticipated that the service will begin in 2013, she said.
The three MTC members who voted against the project were Berkeley Mayor Tom Bates, San Francisco Supervisor Chris Daly and Sue Lempert, who represents the cities of San Mateo County.
Supporters of the project, who include many union leaders and members as well as the Oakland Chamber of Commerce and other business groups, told MTC commissioners at a two-and-a-half-hour hearing today that the light rail system will move passengers to the airport more quickly than the current Air-BART bus service, which is subject to traffic gridlock.
They also said it will create jobs for construction workers, many of whom are now unemployed.
Barry Luboviski, the secretary-treasurer of the Building and Trades Council of Alameda County, said the regional money is "an appropriate use of funds" and "would address severe unemployment in the Bay Area."
Luboviski said, "Our unions are experiencing an unprecedented level of unemployment" and the unemployment rate is as high as 25 percent in some unions.
But project opponents, who include many public transit advocates who favor bus service over rail service, said it's irresponsible for BART to build the airport connector when it faces a projected budget deficit of at least $250 million over the next four years.
They said BART could save hundreds of millions of dollars by using a rapid bus service from the Coliseum station to the airport because they estimate that such a service would only cost between $45 million and $60 million.
Rebecca Slatzman of TransForm, an Oakland-based public transit advocacy group, said she thinks that far few riders would use the airport connector than the 13,000 daily riders that BART initially project.
BART directors approved the airport connector play in a 7-1 vote on May 14.
The pool of money approved by the MTC today includes $70 million in federal stimulus funds that are slated for the Bay Area.
BART's plan calls for borrowing up to $150 million from the federal government.
Another funding source is to raise $44 million by taxing airplane tickets for flights in and out of Oakland's airport. The Port of Oakland has approved the tax.
Some speakers and some MTC commissioners suggested waiting until September before voting on the $140 million in regional funding, saying more time is needed to study the issue.
But MTC Executive Steve Heminger said it was time to vote one way or the other today.
"In my opinion, 20 years isn't a rush," Heminger said. Daly said he's against the airport connector because he doesn't think an engineer taking a fresh look at the project today would think it's the best use of transit funds.
He said, "It's a 1995 project for 2009" because circumstances have changed since the connector was first proposed.
Bates said he's against the connector because "it's a lot of money for a small project."
He said, "It's way overpriced and overvalued."
Marin County Supervisor Steve Kinsey, the MTC's chair, said he's concerned about the cost of the project but said the MTC should approve the funding and let BART make the final decision about whether it should go forward.
"The issue will have to rest with the BART board, not the MTC, and they should take the responsibility," Kinsey said.