The Senate confirmed Brouillette as deputy secretary of the Energy Department in August 2017.
"I want to thank Secretary of Energy Rick Perry for the outstanding job he has done. He will be leaving at the end of the year to pursue other interests. Rick was a great Governor of Texas and a great Secretary of Energy," Trump tweeted.
"He is also my friend! At the same time, I am pleased to nominate Deputy Secretary Dan Brouillette to be the new Secretary of Energy. Dan's experience in the sector is unparalleled. A total professional, I have no doubt that Dan will do a great job!"
Perry announced his resignation Thursday evening in a YouTube video. He didn't specify the date of his departure.
Brouillette wished Perry luck Friday as he moves on in his career.
"Under your leadership, we've achieved true energy independence and have shared the benefits of this success story with the American people and the world," he tweeted.
Trump said he was not surprised by Perry's decision stating he had been informed of the secretary's plans to depart the White House six months ago.
The announcement of his resignation came a week after House Democrats issued Perry a subpoena for documents as part of its ongoing impeachment probe into Trump.
The House Democrats said in a letter to Perry that they are seeking documents concerning what role he may have played in "conveying or reinforcing the President's stark message to the Ukrainian President" concerning the withholding of promised military assistance exchange unless they investigate Trump's political opponent, former Vice President Joe Biden and his son Hunter Biden.
House Democrats are also seeking to answer whether Perry pressured Ukrainian officials "to change the management structure at a Ukrainian state-owned energy company" for the benefit of people Trump's personal attorney, Rudy Giuliani, allegedly asked to participate in the scheme to interfere with the 2020 presidential election.
"The president is entitled to have whoever he wants to work," Mulvaney said.
Perry, who served as governor of Texas from 2000 to 2015, was confirmed by the Senate as Trump's secretary of energy in March 2017.
Daniel Uria and Darryl Coote contributed to this report.