The organizing resolution was passed along a party line vote after a nearly 13-hour session.
The Senate passed Majority Leader Mitch McConnell's resolution laying out a blueprint for President Donald Trump's impeachment trial along party lines early Wednesday after a daylong back-and-forth between House prosecutors and lawyers for the White House.
The Republican majority had earlier voted down several amendments proposed by Senate Minority Leader Chuck Schumer, D-N.Y., to subpoena documents and call witnesses.
The vote came just before 2 a.m. Wednesday and after Rep. Jerry Nadler, D-N.Y., suggested senators were voting for a "cover-up," something that drew sharp responses from the president's legal counsel.
Chief Justice John Roberts admonished both House managers and Trump's counsel, "in equal terms to remember that they are addressing the world's greatest deliberative body."
"I do think those addressing the Senate should remember where they are," Roberts said.
Under the terms of the organizing resolution passed by the Senate, the House case managers will have 24 hours over three days to make their arguments for why the president should be removed from office on charges of abuse of power and obstructing Congress.
Lawyers for the White House will likewise have 24 hours over three days to state their case about why Trump should be acquitted on the two articles of impeachment.
Senators will then have a total of 16 hours to submit questions to both sides before they decide whether to call witnesses or subpoena documents.
The resolution also allows both sides to file motions not related to witnesses or documents by 9 a.m. Wednesday.
The McConnell plan had been opposed by Democrats, who wanted a guarantee they would be able to call witnesses and demand documents that the administration withheld during the House impeachment inquiry.
The vote wasn't a total loss for Democrats, however. McConnell changed two contested provisionsin the rules at the last minute that would have required both sides to make their 24 hours of arguments in just two days and another that could have barred evidence gathered by the House.
Democrats complained that the two-day limit would have meant that they would be making the arguments until 1:00 a.m. or later, depriving much of the public from being able to watch the proceedings.
The other provision could have barred all the evidence against Trump gathered by the House Democrats' inquiry from being entered into the Senate record.
Under the resolution read into the record Tuesday, the evidence now will be admitted automatically unless there's an objection, rather than requiring a proactive vote to admit it.
The House case managers are expected to begin their opening arguments Wednesday afternoon.