Bids are expected by the end of the summer with construction to begin soon after, officials said.
"We're expecting everyone in Leverett to have access to this network by 2014," said Peter d'Errico, a member of the town's Select Board and a leading supporter of the municipal fiber-optic system.
The Proposition 2½ debt exclusion override was favored by a margin of 462-90, with one blank. The 83.5 percent vote to support the project was well above the two-thirds majority needed to approve the override.
Slightly more than 39 percent of the town's 1,405 registered voters cast ballots, which is a large turnout for a single-issue election, town officials said.
"I've been monitoring elections here for nearly 20 years, and this is a very strong turnout," said D'Ann Kelty, the assistant town clerk in Leverett who was in charge of Saturday's special election. "This shows that the town was really invested in this."
Saturday's vote was the final stage of the approval process for the broadband network, which was supported 306-33 at the April 28 Town meeting.
The proposal was developed by the Leverett Broadband Committee after an extended study. Supporters said they were happy with the vote to finance the project.
"This was clearly a mandate to proceed," said d'Errico. "There was vigorous discussion at every stage of the process and it's a sign that community is ready to take charge of its own services."
The 20-year bond measure is expected to increase property taxes by about 6 percent.
However, supporters of the municipal networks expect the savings on telephone and Internet bills will outweigh the tax increase for a majority of the town's residents.
"We wanted people to do the math for themselves, and generally they were satisfied with what they saw," said Richard Nathhorst, a member of the Broadband Committee.
The town will now hire a private company to install a fiber-optic network that will connect with every home in Leverett, making broadband Internet, telephone and television service available to all residents.
The lack of adequate Internet access has created problems for many residents with work and school.
"We have a number of competitive local exchange carriers, or 'CLECs,' here in the Pioneer Valley that we want to reach out to," says Nathhorst. "This will be a public process all the way."