The ballot question asked for voter permission to use 17.5 percent of an existing one-cent sales tax to meet a monthly construction loan payment.
The vote total was 779 for the plan and 297 against, meaning the question passed with 73 percent voter support.
Only 16 percent of registered voters turned out for the election.
Following an October jail inspection, the state served notice that, unless a plan was in place to build a new jail, it would file suit in six months to close the existing jail, which has failed for years to meet state standards.
The county hopes to build a new jail to house 24 prisoners for $2.1 million dollars.
Now that the jail financing plan has been approved by voters, final drawings for the new facility can be completed and the county can seek bids on the project.