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Democrats won both Georgia Senate seats 鈥� and with them, the United States Senate majority 鈥� as final votes were counted Wednesday, serving President Donald Trump a stunning defeat in his last days in office while dramatically improving the fate of President-elect Joe Biden鈥檚 progressive agenda.

Jon Ossoff and Raphael Warnock, Democratic challengers who represented the diversity of their party鈥檚 evolving coalition, defeated Republicans David Perdue and Kelly Loeffler two months after Mr. Biden became the first Democratic presidential candidate to carry the state since 1992.

Mr. Warnock, who served as pastor for the same Atlanta church where civil rights leader Martin Luther King Jr. preached, becomes the first African American from Georgia elected to the Senate. And Mr. Ossoff becomes the state鈥檚 first Jewish senator and, at 33 years old, the Senate鈥檚 youngest member.

Their success is a symbol of a striking shift in Georgia鈥檚 politics as the swelling number of diverse, college-educated voters flex their power in the heart of the Deep South.

This week鈥檚 elections mark the formal finale to the turbulent 2020 election season. The unusually high stakes transformed Georgia, once a solidly Republican state, into one of the nation鈥檚 premier battlegrounds for the final days of Mr. Trump鈥檚 presidency 鈥� and likely beyond.

In an emotional address early Wednesday, Mr. Warnock vowed to work for all Georgians whether they voted for him or not, citing his personal experience with the American dream. His mother, he said, used to pick 鈥渟omebody else鈥檚 cotton鈥� as a teenager.

鈥淭he other day, because this is America, the 82-year-old hands that used to pick somebody else鈥檚 cotton picked her youngest son to be a United States senator,鈥� he said. 鈥淭onight, we proved with hope, hard work, and the people by our side, anything is possible.鈥�

In an interview with ABC鈥檚 鈥淕ood Morning America,鈥� he described his win as a 鈥渞eversal of the old Southern strategy that sought to divide people.鈥�

Ms. Loeffler remains a Georgia senator until the results of Tuesday鈥檚 election are finalized, returned to Washington on Wednesday morning to join a small group of senators planning to challenge Congress鈥� vote to certify Mr. Biden鈥檚 victory.

Georgia鈥檚 other runoff election pitted Mr. Perdue, a former business executive who held his Senate seat until his term expired on Sunday, against Mr. Ossoff, a former congressional aide and journalist.

鈥淭his campaign has been about health and jobs and justice for the people of this state 鈥� for all the people of this state,鈥� Mr. Ossoff said in a speech broadcast on social media Wednesday morning. 鈥淲hether you were for me, or against me, I鈥檒l be for you in the U.S. Senate. I will serve all the people of the state.鈥�

Mr. Trump鈥檚 false claims of voter fraud cast a dark shadow over the runoff elections, which were held only because no candidate hit the 50% threshold in the general election. He attacked the state鈥檚 election chief on the eve of the election and raised the prospect that some votes might not be counted even as votes were being cast Tuesday afternoon.

Republican state officials on the ground reported no significant problems.

Both contests tested whether the political coalition that fueled Mr. Biden鈥檚 November victory was an anti-Trump anomaly or part of a new electoral landscape. To win in Tuesday鈥檚 elections 鈥� and in the future 鈥� Democrats needed strong African American support.

Drawing on his popularity with Black voters, among other groups, Mr. Biden won Georgia鈥檚 16 electoral votes by about 12,000 votes out of 5 million cast in November.

Mr. Trump鈥檚 claims about voter fraud in the 2020 election, while meritless, resonated with Republican voters in Georgia. About 7 in 10 agreed with his false assertion that Mr. Biden was not the legitimately elected president, according to AP VoteCast, a survey of more than 3,600 voters in the runoff elections.

Election officials across the country, including the Republican governors in Arizona and Georgia, as well as Mr. Trump鈥檚 former attorney general, William Barr, have confirmed that there was no widespread fraud in the November election. Nearly all the legal challenges from Mr. Trump and his allies have been dismissed by judges, including two tossed by the Supreme Court, where three Trump-nominated justices preside.

Publicly and privately, some Republicans acknowledged that Mr. Trump鈥檚 monthslong push to undermine the integrity of the nation鈥檚 electoral system may have contributed to the GOP鈥檚 losses in Georgia.

鈥淚t turns out that telling the voters that the election was rigged is not a great way to turn out your voters,鈥� said Utah Sen. Mitt Romney, a Republican and a frequent Trump critic.

Even with Mr. Trump鈥檚 claims, voters in both parties were drawn to the polls because of the high stakes. AP VoteCast found that 6 in 10 Georgia voters say Senate party control was the most important factor in their vote.

Turnout exceeded both sides鈥� expectations.

Even before Tuesday, Georgia had shattered its turnout record for a runoff with more than 3 million votes by mail or during in-person advance voting in December. Including Tuesday鈥檚 vote, more people ultimately cast ballots in the runoffs than voted in Georgia鈥檚 2016 presidential election.

Many in Georgia鈥檚 large African American community were ecstatic when they awoke to news of Mr. Warnock鈥檚 win on Wednesday.

Tracey Bailey, an assistant community manager at an apartment complex in downtown Atlanta, said she jumped for joy.

鈥淚t鈥檚 going to be great for Georgia, and it鈥檚 going to be great for our Black community as a whole,鈥� she said. 鈥淚 think he鈥檚 going to be a fair guy for the people, and that鈥檚 for all people.鈥�

This story was reported by The Associated Press. Peoples reported from New York. Bynum reported from Savannah, Ga. AP writers Haleluya Hadero, Angie Wang, Sophia Tulp, Ben Nadler, and Kate Brumback in Atlanta contributed to this report.