The 230,000-square-foot facility, which is under construction on Chamblin Road, is scheduled to open in 2009.
The board supported the proposal by a 4-0 vote.
Board member Mike Sleeper abstained, saying he would like more time to think about a name before making a decision. Grovetown was one of seven names that was suggested for the board's consideration at the meeting.
Roxanne Whitaker, who was unanimously approved as the board's vice chairwoman for this year, said most of the students who will attend the new high school live in Grovetown or have a Grovetown ZIP code.
"It just gives it that hometown feeling," she said.
Superintendent Charles Nagle said that once rezoning plans have been finalized, a lot of the school's students won't have Grovetown addresses.
The board hopes to approve rezoning plans for the school by spring.
The facility, which has a three-tiered, split-level design, will hold 1,250 to 1,500 students.
Mr. Nagle said Grovetown was a "historically and geographically descriptive" name.
According to research provided to the board by Barry Paschal, the publisher of The Columbia County News-Times , the county had a Grovetown High School from at least the early 1900s until the 1940s.
Grovetown High, along with Central and Leah schools, eventually moved its upper grades to Harlem High and became a primary school only.
"I think that will make a lot of people happy in the Grovetown area," Mr. Nagle said after the meeting.
Other names presented to the board included Liberty, or Liberty Park; Horizon; Central; Euchee Creek; Philadelphia and Sardis.
Reach Betsy Gilliland at (706) 868-1222, ext. 113, or firstname.lastname@example.org.