Ossoff declared victory Wednesday morning in his race against Perdue.

While ABC News has not yet projected the race, Ossoff has garnered a significant lead overnight and his margin is now nearly 5,000 votes greater than President-elect Joe Biden's was over President Donald Trump in November.

"It is with humility that I thank the people of Georgia for electing me to serve you in the United States Senate," Ossoff said in video statement. "Thank you for the confidence and trust that you have placed in me."

Ossoff, as he has throughout his campaign, lamented the toll of the coronavirus pandemic and stressed the importance of the country getting a grip over the deadly virus.

"I will work in the U.S. Senate to support a robust public health response so that we can defeat this virus, putting Georgia's own Centers for Disease Control and Prevention in the lead, trusting medical expertise, doctors, and scientists to bring the tools to bear, the technology to bear, the ingenuity to bear, and the resources to bear necessary to stop the spread of this virus to defeat it and to get our daily lives back -- and to rush direct economic relief to people who need help right now," he said.

Despite the bitter race with Perdue, Ossoff promised to be a senator for all Georgians.

"I want to thank the people of Georgia for participating in this election, everybody who cast your ballot, everybody who put your faith and confidence in our democracy's capacity to deliver the representation that we deserve, whether you were for me, or against me, I'll be for you in the U.S. Senate," he said. "I will serve all the people of the state," he said. "I will give everything I've got to ensuring that Georgia's interests are represented in the U.S. Senate."

Warnock called his projected victory a "historic moment," saying he "can't wait" to be in the upper chamber of Congress "to represent the concerns of ordinary people."

"I'm deeply honored that the people of Georgia decided to place their faith in me and have decided to send me to represent their interests in Washington, D.C.," Warnock told ABC News Chief Anchor George Stephanopoulos in an interview Wednesday on "Good Morning America."

"Certainly, this is a historic moment and I'm just deeply grateful to be a vessel in a moment in which we're facing such large problems in our country," he added, "and I can't wait to get to the U.S. Senate to represent the concerns of ordinary people."

Warnock, a senior pastor of the Ebenezer Baptist Church in Atlanta, the former pulpit of the Rev. Martin Luther King Jr., is the first Black senator Georgia has elected and only the 11th Black senator elected in U.S. history.

"Georgia is in such an incredible place when you think about the arc of our history, we are sending an African-American pastor of Ebenezer Baptist church where Martin Luther King Jr. served," he said. "This is the reversal of the old southern strategy that sought to divide people. In this moment we've got to bring people together in order to do the hard work and I look forward to doing that."

When asked about his top priority for this year in the Senate, Warnock said -- as he has throughout his campaign -- that the country needs to get the coronavirus pandemic under control.

"Like so many Americans, as we witnessed the incredible death toll over 350,000 Americans lost lives, lost livelihoods, we need a national strategy that takes this virus seriously, that gets the vaccine distributed safely and efficiently," he said. "We've got to re-open our economy, get our kids safely back to school and we got to make sure that people know that they will have their health care, particularly in the middle of a pandemic."

-ABC News' Quinn Scanlan

Warnock's edge over Loeffler continued to grow Wednesday morning and is now too big for the incumbent Republican senator to request a recount.

Warnock currently leads by 53,430 votes, which is a margin of 1.2% of all votes cast in the race.

ABC News projected just before 2 a.m. ET that Warnock will win.

-ABC News' Quinn Scanlan

Ossoff's edge over Perdue has grown significantly, with votes coming in from the Democratic stronghold of DeKalb County. But that margin is still within recount territory.

With 98% of the expected vote reporting, Ossoff leads with 50.2% -- 2,208,717 ballots -- while Perdue trails behind with 49.8% -- 2,192,347 ballots.

Ossoff's lead of 16,370 votes is now greater than that of President-elect Joe Biden's over President Donald Trump in Georgia (11,779 votes).

The margin is currently 0.4%, and if it remains less than 0.5%, Perdue would be entitled to request a machine recount after the results are certified.

-ABC News' Quinn Scanlan

More than 3 million voters in the Georgia runoff elections cast their ballots early -- 1,018,381 by mail and 2,074,994 early in-person -- according to Georgia Votes, already a record-setting figure for runoff elections.

The total early vote so far also includes 123,079 who did not participate in November's general election -- which is 35,000 more votes than the margin that separated Sen. David Perdue and Jon Ossoff the first time around, when the incumbent Republican edged out his challenger by just over 88,000 votes. Sen. Kelly Loeffler and Raphael Warnock were competing in a jungle primary in which the large field diluted their vote shares.

The secretary of state's office won't have Tuesday's in-person turnout numbers until at least 1 p.m. on Wednesday when counties are required to report how many ballots they received Tuesday in order to calculate the number of outstanding ballots. It may take days for the final results to become available depending on how close the races are.

Republicans are relying on high Election Day turnout, believing close to a million votes on Tuesday is likely their path to victory. At a rally in Dalton on Monday night, President Donald Trump signaled how many votes Republicans are eyeing: "I guess we have to get over a million votes tomorrow, right, Kelly? Over a million. All right. That's a lot of votes, Kelly, but we'll do it."

-ABC News' Quinn Scanlan, Kendall Karson and Meg Cunningham