Bill Taylor, the top US diplomat in Ukraine, told impeachment hearings he had a "clear understanding" aid would be withheld pending an investigation.
Mr Trump denies there was any threat.
Public impeachment hearings will begin next Wednesday, with Mr Taylor set to be the first witness called.
Mr Taylor testified in closed door impeachment hearings last month, and a transcript of his evidence was released to the public on Wednesday.
He told a Congressional committee that two state department officials said Mr Trump would not "sign a check" for nearly $400m (£311m) in US military aid until Ukrainian officials announced an investigation into Democratic presidential contender and former vice president Joe Biden.
Mr Biden's son Hunter Biden previously sat on the board of the Ukrainian oil company Burisma. President Trump has claimed without evidence that Joe Biden used his position as vice president to quash an investigation into Burisma.
Mr Taylor also told the Congressional committee that Mr Trump's personal lawyer, Rudy Giuliani, was behind the drive to get Ukraine to announce an investigation into the Bidens.
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Mr Taylor's testimony follows evidence from Gordon Sondland, an ally of President Trump who is the US ambassador to the European Union, who told the impeachment hearings that he informed a Ukrainian official of a quid pro quo – US military aid in exchange for an investigation announcement. He testified that a White House visit for the Ukrainian president was also part of the deal.
Mr Sondland returned to Congress to revise earlier testimony, in which he denied that any preconditions had been placed on the delivery of aid.
Critics of Mr Trump say that any quid pro quo would be a clear violation of president ethics, because it uses the power and office of the presidency in an attempt to damage a domestic political rival. Mr Trump denies that there was any quid pro quo.
Impeachment goes public
Congressional Democrats announced on Wednesday that the first public hearings of the inquiry would take place next Wednesday. Three state department officials, including Mr Taylor, will testify first. So far, lawmakers from three key Congressional committees have heard from witnesses behind closed doors.
House Intelligence Committee chairman Adam Schiff, who is overseeing the inquiry, told reporters on Wednesday that the evidence for presidential wrongdoing was growing.
He said: "We are getting an increasing appreciation for just what took place during the course of the last year – and the degree to which the president enlisted whole departments of government in the illicit aim to get Ukraine to dig up dirt on a political opponent."
The Capitol Hill hearings will be broadcast live, with both Democratic and Republican lawmakers questioning witnesses.
On Wednesday – a week ahead of his scheduled public hearing – House Democrats released a transcript of Mr Taylor's evidence. It showed the diplomat told lawmakers it was his "clear understanding" that the president had withheld US military aid because he wanted Ukraine to investigate the Bidens.
The military aid to Ukraine was eventually released in September, after a whistleblower raised the alarm about a 25 July phone call in which Mr Trump asked the Ukrainian president to investigate the Bidens. The Department of Justice, led by the attorney general, Bill Barr – a key Trump ally – initially attempted to prevent the whistleblower complaint being passed to congress, but it was subpoenaed by House Democrats.
The transcript in black and white
By Jon Sopel, BBC North America editor
Seeing it in black and white lays it out very clearly. The US military aid – plus a visit to the White House for the Ukrainian president – was the prize. But there would be no prize if the Ukrainians did not announce an investigation into the Bidens.
The other thing you get from this transcript is the sense of shock that seasoned officials like Bill Taylor had, this sense that all normal rules had been suspended, that these dealings were all going through a side channel led by the president's personal lawyer Rudy Giuliani, and the State Department was playing no role in it.
Then you see Taylor's utter astonishment at the idea that military aid – aid vital to the Ukrainians – was going to be withheld, out of the blue. He's on a call and suddenly he hears, "We're stopping it". The transcript of his evidence is shocking, and it sets the stage for blockbuster hearings next week.
Quick facts on impeachment
Impeachment is the first part – the charges – of a two-stage political process by which Congress can remove a president from office. If, following the hearings, the House of Representatives votes to pass articles of impeachment, the Senate is forced to hold a trial.
A Senate vote requires a two-thirds majority to convict and remove the president – unlikely in this case, given that Mr Trump's party controls the chamber.
Only two US presidents in history – Bill Clinton and Andrew Johnson – have been impeached, but neither was convicted. President Richard Nixon resigned before he could be impeached.
