The Trump administration is all but certain to appeal both rulings, a process that could tie up the testimony and records in courts for many months. Democrats have made clear that they are unwilling to wait for that process to play out, meaning their inquiry may simply never benefit from any information that may come to light.

“We will not allow the president or others to drag this out for months on end in the courts,” Mr. Schiff wrote on Monday, expressing confidence in the case in hand.

His committee has already collected dozens of hours of testimony supporting the underlying allegation at the center of the impeachment inquiry: that the president used the powers of his office to pressure Ukraine to discredit his political rivals by announcing investigations into former Vice President Joseph R. Biden Jr. and an unsupported theory that Democrats conspired with Ukraine to interfere in the 2016 election.

“As the evidence conclusively shows, President Trump conditioned official acts — a White House meeting desperately desired by the new Ukrainian president and critical U.S. military assistance — on Ukraine announcing sham, politically motivated investigations that would help President Trump’s 2020 re-election campaign,” Mr. Schiff said, encapsulating what is likely to be the core of the Democrats’ report.

Mr. Schiff did not put a precise date on the delivery of his report to the Judiciary Committee, but the rough timeline he outlined would put Democrats on track to vote on impeachment articles by the end of the year, barring unexpected complications or a collapse in support within their caucus. If they are successful, a trial to determine whether Mr. Trump will be acquitted or removed from office would follow in the Senate.

At this point, Democrats expect to get little to no Republican support in the House. The president’s allies have united firmly behind him to argue either that the facts laid out by senior diplomats and administration officials are incorrect or that they simply do not merit impeachment.

The Judiciary Committee is expected in the coming days to announce public impeachment hearings to take place next week to hear the evidence on Ukraine and to begin to draft and debate impeachment articles, which are roughly analogous to charges in a courtroom trial. They could also convene sessions with expert witnesses to define impeachable offenses and offer Mr. Trump and his legal team a chance to present a defense or exculpatory evidence.