The choice of Perry adds to the list of oil-drilling advocates skeptical about climate change who Trump has picked for senior positions in his Cabinet, worrying environmentalists but cheering an industry eager for expansion.
The selection of Perry, who also had been mentioned as a candidate for agriculture secretary, was disclosed on Monday night after Perry met the president-elect at Trump Tower in New York.
The department is responsible for U.S. energy policy and oversees the nation's nuclear weapons program. Perry has advocated lighter regulation on the fossil fuel industry, and has called the science around climate change "unsettled."
Perry's proposal to get rid of the Energy Department caused what has become known as his "oops" moment during a November 2011 Republican presidential candidate debate when he could not remember all of the three Cabinet-level departments he wanted to eliminate. After mentioning the departments of Commerce and Education, he said, "I can't. The third one, I can't. Sorry. Oops."
A few minutes later in the debate Perry said with a laugh, "By the way that was the Department of Energy I was reaching for a while ago."
Perry, who also briefly ran in the 2016 presidential race, would have to be confirmed by the Senate to head the Energy Department.
Perry served as governor of Texas, a leading oil-producing state, from 2000 when he succeeded President George W. Bush until 2015. In his unsuccessful presidential runs, he touted his record of job creation in the second-most-populous state.
Perry was a fierce critic of Trump last year before dropping out of the race, calling him "a cancer on conservatism" who offered "a toxic mix of demagoguery and mean-spiritedness and nonsense."
Trump also had harsh things to say about Perry during the campaign, even belittling his eyeglasses by saying, "He put on glasses so people will think he's smart."
Once Trump secured the nomination, Perry endorsed him as "the people's choice."
There were indications of a possible rocky handover for the Energy Department after Trump transition officials asked the agency for the names of employees who have worked on climate change issues. Department spokesman Eben Burnham-Snyder said on Tuesday the department will not comply and that the request had "left many in our workforce unsettled."
Perry's selection is another indication that the incoming Trump administration may be friendly toward the fossil fuel industry. He is on the board of directors for Energy Transfer Partners, the company building the Dakota Access Pipeline in North Dakota that has been stalled by protests by the Standing Rock Sioux tribe and supporters.
Trump on Tuesday named Rex Tillerson, chief executive of oil giant Exxon Mobil Corp, as his choice for secretary of state.
Trump has settled on U.S. Representative Cathy McMorris Rodgers, a climate-change skeptic and an advocate for expanded oil and gas development, as interior secretary.
Trump's choice for the Environmental Protection Agency is Oklahoma Attorney General Scott Pruitt, an ardent opponent of President Barack Obama's measures to curb climate change who has sued the EPA to block in a bid to undo a key regulation to curb greenhouse gas emissions, mainly from coal-fired power plants.
An overwhelming majority of scientists believe that carbon dioxide emissions from burning oil, gas and coal is a significant contributor to global climate change, causing sea level rise, drought and more frequent violent storms.
The Energy Department was established by President Jimmy Carter in 1977 after an embargo by oil-exporting nations led to shortages in the United States.
Billionaire environmental activist Tom Steyer said he hoped Perry's nomination would be blocked.
"Trump no longer has to abolish departments. He can dismantle them from within," Steyer said. "It’s now up to the Senate to defend our health, our economy and our democracy by defeating this nomination."