Georgia Democratic Senate candidates Raphael Warnock (R) and Jon Ossoff (L) bump elbows during a “It’s Time to Vote” drive-in rally on December 28, 2020 in Stonecrest, Georgia.Jessica McGowan | Getty ImagesDemocrats took control of the Senate on Wednesday when three new members of the party were sworn in, giving a boost to President Joe Biden’s ambitions in the White House.The party now controls the presidency and both chambers of Congress.Democratic Sens. Raphael Warnock and Jon Ossoff of Georgia and Alex Padilla of California took office, bringing the Senate party split to 50-50. Newly inaugurated Vice President Kamala Harris, who will hold the chamber’s tiebreaking vote, briefly presided over the chamber and swore in the three senators. She laughed when she read a message describing her own resignation, quipping, “That was very weird.”The narrow Democratic majority will help Biden as he tries to fill out his Cabinet and pass an agenda headlined by a coronavirus relief package. Though Senate Majority Leader Chuck Schumer and Democrats will decide what the Senate pursues, they face a challenge in finding Republican support to pass most legislation.”We have a lengthy agenda, and we need to get it done together. … This will be an exceptionally busy and consequential period for the United States Senate,” Schumer said in his first speech as majority leader.The New York Democrat said the Democratic Senate will “do business differently,” moving to address coronavirus relief, systemic racism and climate change.Speaking after Schumer, Senate Minority Leader Mitch McConnell, R-Ky., said “I congratulate my friend from Delaware and look forward to working with him as our new president wherever possible.” He noted that the election left Democrats with narrow majorities in both the Senate and House, interpreting it as a signal that voters did not endorse sweeping change.Sen. Patrick Leahy, D-Vt., also became president pro tempore of the Senate on Wednesday. The 80-year-old is now third in the presidential line of succession, after Harris and House Speaker Nancy Pelosi, D-Calif.Warnock, 51, and Ossoff, 33, won special elections earlier this month that determined control of the Senate. They will become the first Black and Jewish senators, respectively, from Georgia.Schumer noted that Warnock was born when two “staunch segregationists” represented Georgia in the Senate.Padilla, 47, was appointed by Gov. Gavin Newsom to fill Harris’ Senate seat when she resigned to become vice president. He becomes the first Latino senator from California.Ossoff posted photos of the Georgia senators-elect at the presidential inauguration ceremonies on Wednesday. He wrote along with them, “Change has come to Georgia. Change is coming to America.”Schumer and McConnell have to come to an agreement on how to carry out Senate business in the coming weeks. They will need a power-sharing accord to decide how many members each party has on committees and how those panels resolve ties.McConnell’s office has said that, as part of a deal, he wants to ensure the Senate preserves the filibuster. Some Democrats have called to get rid of the tool to allow bills to pass with a simple majority vote.The Senate also has to set a structure for an impeachment trial for former President Donald Trump. The House charged him with inciting an insurrection at the U.S. Capitol on Jan. 6 but has not yet sent the impeachment article to the Senate.Biden hopes the Senate can spend part of its time on the impeachment trial while still confirming executive branch nominees.Subscribe to CNBC on YouTube.