The goat was among 15 other animals on the ballot in the running for the honorary position. Lincoln beat out several other animals, including cat Sassy Towle, a dog named Stella Heibler and a gerbil named Crystal, for the job.
Lincoln took 13 of the 53 votes cast, just surpassing a dog named Sammie Viger who took home 11.
As mayor, Lincoln will be expected to attend local and major events, including the Memorial Day parade, for which he'll wear a custom sash.
Fair Haven doesn't have a human mayor. Town Manager Joe Gunter told the Rutland Herald he got the "great idea" to elect an animal to office from a small town in Michigan.
He said he figured the election would be a good way to raise money to create a local playground. It only raised about $100 through a $5 entry fee, but it reportedly provided other benefits.
"It turned into a good civics lesson," he told the news outlet. "Get the kids involved in town government. (I) thought this was a great way to break the ice with the kids."
Lincoln is set to take office on Tuesday.
The Associated Press contributed to this report.