This story was updated May 1, 2018, at 11:59 p.m.
Coppinger ran unopposed in the Republican primary. He received 11,468 votes. Brown, 40, of Lookout Mountain, received 4,998 votes, defeating Love, who received 1,845 votes.
It is Brown's first run for political office.
"I'm incredibly grateful to win the support of my party in one of this year's most crucial elections," she said. "And I'm eager to continue to deliver our message to every voter in Hamilton County."
Brown manages a nonprofit financial services organization and said her experience with multimillion-dollar accounts will help her manage the county's budget. She wants to improve schools, upgrade public safety and infrastructure, and implement criminal justice reform. If elected, she would be the county's first female mayor.
Coppinger is the current mayor and oversees a budget of nearly $725 million and more than 1,700 employees. The Hixson High School graduate and former Chattanooga State and University of Tennessee at Chattanooga student was elected mayor in 2012.
He was previously a county commissioner from 2006 until his mayorship.
Coppinger touts that the county has added more than 14,000 jobs and $2.2 billion in new investment since his election.
"The reason I entered public service to begin with is to work to make this county a great place to live, work, raise a family, retire and even vacation," Coppinger said. "I remain committed to that purpose."
The mayor's salary in 2017 was $163,445.
Countywide, 20,498 ballots were cast. There are 192,662 eligible voters.
More than 10,000 people voted in the last mayoral Republican primary in 2014 when Coppinger won more than 90 percent of the vote to defeat GOP challenger Basil Marceaux. The Democratic primary that year had 4,000 voters, but no one qualified to run for the position.