Two Georgia Democrats were sworn in Wednesday as the newest members of the US Senate, handing their party control of the upper chamber just hours after President Joe Biden took office.

With Jon Ossoff and Raphael Warnock -- who ousted two Republicans in a pair of January 5 run-offs -- being formally seated, the body now stands deadlocked at 50-50.

That means Democrats control the chamber because new Vice President Kamala Harris acts as the tie-breaking vote.

Harris, herself a former senator from California, presided over the session just hours after becoming vice president, and swore in the two Georgia men and her own replacement, Alex Padilla.

By flipping the Senate and holding the House of Representatives in last November's election, Democrats now control all levels of power in Washington in a period of heightened political partisanship following the four-year presidency of Donald Trump.

That provides Biden an avenue to push through some of his key legislative priorities on climate change, immigration, and a $1.9 trillion relief package to help American families and businesses devastated by the coronavirus pandemic.

The Democratic shift means top Republican Senator Mitch McConnell cedes power to his rival, Senator Chuck Schumer, who becomes the first-ever majority leader born in the state of New York.

In his first speech leading the Senate, the 70-year-old Schumer described himself as "a kid from Brooklyn, the son of an exterminator and a housewife, a descendant of victims of the Holocaust."

Senate control should mean Biden will have an easier time getting his cabinet members and judge picks confirmed. But passing aggressive legislation is likely to be a far more difficult proposition.

Schumer nevertheless sounded a note of high optimism about the future now that Trump, who incited a mob of his supporters to storm the US Capitol two weeks ago in a bid to prevent the certification of Biden's election win, has exited the White House.

"I would challenge anyone not to feel hopeful today," Schumer said.

"Today, the threat to democracy from the presidency itself has ended, but the challenges we face as a nation remain." 

McConnell congratulated both Biden and Harris on their inaugurations, and said they begin their terms "with the prayers of our whole nation at their backs."

And he specifically noted Biden's call for unity, saying he looked forward to "working with our new president wherever possible."

Among the Democratic Senate's first orders of business: the impeachment trial of Trump, who is no longer president but could face a lifetime ban on serving in public office if he is convicted.