Braintree officials have cleared the way for an ­Amazon delivery center to open, despite concerns about traffic.

The town’s Planning Board voted unanimously on Tuesday night to approve a special permit for the retail giant to put a “last-mile’’ distribution center in an empty warehouse on Campanelli Drive.

The 250,000-square-foot facility would serve as a key link in the company’s growing next-day and same-day delivery service in Greater Boston, a connection between Amazon’s massive shipping center in Fall ­River and customers’ doorsteps.

But it will also put hundreds of cars an hour on some of the South Shore’s busiest streets.

Neighbors of the site in the Braintree Commerce Center and some residents complained that Granite Street and the Five Corners area of Braintree would be clogged with delivery vehicles making their way to and from Route 128.

A traffic study submitted by Amazon described an around-the-clock operation, with trucks delivering goods overnight and fleets of vans and cars — dozens at a time — making trips each morning to shuttle those goods to homes and businesses.

At peak times, an estimated 262 cars would come and go each hour.

To help ease the traffic worries, Amazon has agreed to pay $1.2 million for improvements to traffic signals in the area, and it may add lights at other intersections.

That and various other promises were enough to satisfy Planning Board officials, who voted unanimously to approve the permit.

Opponents have 21 days to appeal the decision.

Tim Logan can be reached at tim.logan@globe.com. Follow him on Twitter at @bytimlogan.