Democratic Senate candidate Rev. Raphael Warnock
Credit: ERIK S LESSER/EPA-EFE/Shutterstock
Her opponent, Mr Warnock, 51, is pastor of the Atlanta church where Martin Luther King Jr preached.
If elected, Mr Warnock would become Georgia’s first black US senator.
Mr Perdue, 71, is a former business executive, and Mr Ossoff a former journalist who would become the youngest person in the Senate.
In Atlanta voter Kari Callaghan, 37, said she voted "all Democrat" having previously been a Republican.
She said: "I’ve always been Republican but I’ve been pretty disgusted by Trump and just the way the Republicans are working. This isn’t the conservative values that I grew up with."
But Will James, 56, said he didn’t want one party to control the White House and Congress, so he voted Republican.
He said: "I believe in balance of power, and I don’t want either party to have a referendum basically."
More than three million Georgians voted early by post or in-person.
Voters stand in line before the doors open at Cobb County Community Center in Atlanta
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If both Democrats won it would mean the Senate being split 50-50 split.
The vice president, soon to be Kamala Harris, would have the casting vote.
Democrats already hold a narrow majority in the House of Representatives.
For Mr Biden a Democrat-controlled Senate would allow him to quickly push through his agenda. But under Republican control he would have less chance of achieving his goals on issues including expansion of government-backed health care and climate change.
It would also make it more difficult for him to get his Cabinet and judicial nominees confirmed by the Senate.
Mr Biden’s narrow win in Georgia was the first by a Democrat presidential candidate since 1992.
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