Democrat Schumer gave the message directly to the Senate after reaching a compromise with Republicans on the schedule.
The Republicans wanted to give Trump another week or so to prepare his defense.
The charges will now be presented to the Senate on Monday night.
The parties will then have until the second week in February to prepare for the trial, Schumer said.
"Meanwhile, the Senate will continue to address other important issues for the American people, such as the nominations to the government and the corona support package that will help millions of Americans suffering from this pandemic," the majority leader told Reuters.
Trump historically
Republican Senate Leader Mitch McConnell is pleased that Trump has been given more time to prepare, said his spokesman Doug Andres.
"This is a victory for justice and the idea of a proper legal order," said Andres.
Donald Trump will be the first president in US history to be brought to justice after resigning.
He will also be the first to be brought before a Supreme Court twice.
Trump is accused of inciting riots in connection with the storming of the US Congress building Capitolium on January 6.