The House Regulated Industries Committee voted 15-1 to send the legislation to floor vote.
"It didn't take us but five years to get here," said the bill's sponsor, state Sen. John Bulloch.
The Ochlocknee Republican called it "a local-control and democracy bill."
No opponents spoke at Tuesday's hearings but religious groups have argued against the bill, saying it attacks family values by sullying the Sabbath.
The measure - which would allow local governments to ask voters if they want to permit Sunday alcohol sales in stores - has already cleared the state Senate, where it has stalled for the last few years.
Georgia is one of just three states that bans stores from selling alcohol on Sunday. The others are Indiana and Connecticut.
Many restaurants and bars in Georgia can already sell alcohol on Sundays.
Gov. Nathan Deal has said he will sign the measure if it passes. His predecessor, Gov. Sonny Perdue, had threatened to veto it.
The bill is expected to face a House vote next week as the Legislature enters the homestretch of its 2011 session.
If it passes, Sunday sales measures could be on local ballots as soon as this fall.