Carter, who announced his decision Wednesday in an interview with The Atlanta Journal-Constitution, said Georgia "can't afford four more years of an economy that's not working for the middle class and an education system that's underfunded."
"It's not about politics," he told the Journal-Constitution. "It's about making sure we can get the state that we need."
Carter, 38, is the second high-profile Democrat seeking a spot on next year's ballot. Senate candidate Michelle Nunn, the daughter of former U.S. Sen. Sam Nunn, is her party's front-runner in a crowded field wanting to succeed retiring Republican U.S. Sen. Saxby Chambliss.
Carter said he is a fiscal conservative who would revamp an education funding system he characterized as a "shell game" and restore trust in the government.
"We want a Georgia that's at its best," Carter told the Journal-Constitution. "And Georgia at its best invests in education, it doesn't cut billions out of the classrooms, it has an economy that works for the middle class and it always has an honest government."
Of his grandfather, the younger Carter says the two talk, "[but] at the end of the day, this campaign will be about getting Georgia back to where it needs to be."
Deal, who defeated former Gov. Roy Barnes in 2010, already has two GOP primary challengers: Dalton Mayor David Pennington and state Schools Superintendent John Barge.