“There has never been a greater betrayal by a president of the United States of his office and his oath to the Constitution,” the Wyoming representative said, adding that Mr Trump had “summoned this mob, assembled the mob, and lit the flame of this attack”.
Two other Republican House members, John Katko and Adam Kinzinger, said they would also vote for impeachment.
House Republican leader Kevin McCarthy, a Trump ally who has said he opposes impeachment, decided not to ask rank-and-file members of the party to vote against the measure, US media reported.
According to the New York Times, Senate Republican leader Mitch McConnell told confidants he was pleased Democrats wanted to impeach the president because he believed it would help rid the Republican party of Mr Trump.
On Tuesday evening, House Republican Brian Fitzpatrick of Pennsylvania introduced a resolution to censure Mr Trump, a congressional rebuke less severe than impeachment.
The measure accuses Mr Trump of “trying to unlawfully overturn” the results of November’s election and of having “imperilled a coequal branch of Government”.
Earlier, the House passed a resolution by 223-205 votes calling on Vice-President Mike Pence to help oust Mr Trump using the 25th Amendment, which would allow the cabinet to remove the president if he is deemed unable to discharge his duties.