Raphael Warnock will become the first black senator to represent Georgia in the state's history.
The Associated Press has called one race for the Democratic candidate, who currently leads his Republican opponent Kelly Loeffler by 50.5-49.5 with 97 per cent of the votes counted.
Democrats are now within reach of controlling the US Senate, with the results of one more race to determine whether they can control all of Congress.
The other Senate run-off contest remains under way. Republican candidate David Perdue and Democratic candidate Jon Ossoff are tied at 50-50, with 97 per cent of the vote counted and Mr Ossoff leading by around 3,500 votes.
Most of the remaining votes are in Democrat-leaning areas.
The Republicans currently hold 50 seats in the Senate, while the Democrats have 48. If Mr Perdue wins his race, the Republican party will retain control of the chamber.
However, if Mr Ossoff wins, the Senate will split 50-50, giving incoming vice president Kamala Harris the tie-breaking vote and effectively giving Democrats complete control of the federal government.
Democrats must win both Georgia races to seize Senate control from the Republicans. Failure to do so would make it much more difficult for incoming President Biden to enact new legislation in a bitterly divided Congress.
The results could be known by Wednesday local time, Georgia Secretary of State Brad Raffensperger told CNN, although the outcome may remain in doubt for days if the margins are razor-thin. Officials were set to begin counting ballots as soon as polls closed at 7pm (11am AEDT), although a handful of sites will stay open later after earlier delays.
Voters endured long lines at some polling sites and had no lines at others.
In Atlanta, Jonathan Temple, 57, said he backed the two Republicans.
“If we lose, we’ll get higher taxes for sure - you can bet on it,” Mr Temple said. “We’ll have a runaway liberal agenda, runaway spending. That’s not good for America.”
Voting in Cobb County outside Atlanta, Roshard Tamplin, 42, said he supported the two Democrats, citing civil rights and voting rights as important issues.
People check in as they prepare to cast their vote at the C.T. Martin Natatorium and Recreation Center on 5 January, 2021 in Atlanta, Georgia. Source: Getty
“They’re trying to make it harder to vote, especially for black people,” Mr Tamplin, who is Black, said of Republicans.
The final days of the tense contests, which set records for campaign spending and early turnout in Georgia, were dominated by Mr Trump’s continued efforts to subvert the presidential election results.
On Saturday, , again falsely claiming massive fraud.
Mr Trump’s efforts to undo his loss - with some Republicans planning to object to the certification of Mr Biden’s win when - have caused a split in his party and condemnation from critics who accuse him of undermining democracy.
Mr Biden, due to take office on 20 January, was the first Democratic presidential candidate to win in Georgia since 1992.
Mr Trump and Mr Biden campaigned in Georgia on Monday. It remains to be seen whether Mr Trump’s claims about election fraud will dissuade Republicans from voting in Georgia, as some in the party have feared.
Democrats control the House of Representatives, with the number of seats allotted to states determined by their population. Democratic control of both chambers could boost Mr Biden’s legislative agenda in areas such as economic relief amid the coronavirus pandemic, climate change policy, healthcare and policing reform.
Historic candidacies
Mr Warnock has become Georgia’s first black US senator and Mr Ossoff, at 33, would be the Senate’s youngest member. Mr Perdue is a former Fortune 500 executive who has served one Senate term.
Mr Raffensperger told Fox News the election results will likely be known on Thursday morning. Mr Raffensperger said Mr Trump’s false claims on voter fraud hurt voter confidence in the runoffs, adding, “I can assure you that it will be a fair and honest election, that it’ll be safe and it’ll be dependable.”
Democratic Senate candidate Reverend Raphael Warnock speaks outside his campaign bus at a canvassing kick off event in Marietta, Georgia, 5 January 2021. Source: AAP
Polls are open until 7pm local time. Some 3 million ballots were cast in early in-person and mail-in voting, mirroring a pandemic-related trend seen in November.
Democrats were encouraged by the early vote, including strong numbers from black voters, seen as crucial to their chances. Republicans have historically turned out in higher numbers on Election Day.
Speaking to reporters in Atlanta, Mr Ossoff said Georgians want equal justice, economic relief, help fighting the pandemic and an end to Washington’s gridlock.
“That’s the kind of change that Georgia voters have been turning out in record numbers to demand,” Mr Ossoff said.
Mr Perdue and Ms Loeffler have supported Mr Trump’s unfounded fraud claims while arguing they represent the last barrier to unrestrained liberalism in Washington.
“We’ll look back on this day if we don’t vote and really rue the day that we turn the keys to the kingdom over to the Democrats,” Mr Perdue, whose current term technically ended on Sunday, told Fox News on Tuesday.
