The documents relate to a call between Mr Trump and Ukrainian President Volodymyr Zelensky on 25 July.
In the call, Mr Trump pushed Mr Zelensky to investigate his leading Democratic political rival, Joe Biden.
The impeachment inquiry stems from the call, which was flagged up by a whistleblower in August.
The whistleblower alleged that Mr Trump used a $400m military aid package to Ukraine, which had been suspended earlier in July, as leverage to persuade Mr Zelensky. The White House released the aid in September.
Mr Trump has denied any wrongdoing, accusing his political opponents of a “witch hunt”.
But in a move to crank up the pressure on the president, the three House committees leading the investigation have given him until 18 October to hand over the documents.
“We deeply regret that President Trump has put us – and the nation – in this position, but his actions have left us with no choice but to issue this subpoena,” the Democrats wrote in a letter to the White House.