Schumer's announcement comes after a request from Senate Minority Leader Mitch McConnell to delay the trial until February and give Trump and his still-forming legal team time to prepare a defense.
The senate majority leader said members would be sworn in on Tuesday and the trial would begin the week of Feb. 8.
"Leader McConnell is glad that Leader Schumer agreed to Republicans' request for additional time during the pre-trial phase," Doug Andres, McConnell's spokesman, said in a statement. "Especially given the fast and minimal process in the House, Republicans set out to ensure the Senate's next steps will respect former President Trump's rights and due process, the institution of the Senate, and the office of the presidency. That goal has been achieved. This is a win for due process and fairness."
Trump will be the first former president to face an impeachment trial. Some Senate Republicans have argued that the trial would be unconstitutional because the 45th president is no longer in office, a stance that could trigger a Senate debate and vote on the validity of the trial in the coming weeks.
"I have spoken to Speaker Pelosi who informed me that the articles will be delivered to the Senate on Monday," Schumer said.
"The Senate will conduct a trial of the impeachment of Donald Trump. It will be a full trial, it will be a fair trial," he added, without details on the length or format of the proceedings.
On Friday afternoon, House Speaker Nancy Pelosi echoed Schumer's comments in a letter sent to her House Democratic caucus, saying Trump will have had plenty of time to prepare for his upcoming Senate trial and responding to Republicans complaints that the House impeachment was rushed.
"The House has been respectful of the Senate's constitutional power over the trial and always attentive to the fairness of the process," Pelosi said in the letter. "When the Article of Impeachment is transmitted to the Senate, the former President will have had nearly two weeks since we passed the Article. Our Managers are ready for trial before the 100 Senate jurors," she wrote.
ABC News' Mariam Khan contributed to this report.