WASHINGTON—President-elect Donald Trump has tapped former Texas Gov. Rick Perry to lead the Energy Department, according to two transition officials, selecting a climate-change skeptic who led the nation’s biggest energy-producing state for nearly 15 years.

If confirmed by the Senate, Mr. Perry would add a steadfast conservative politician to Mr. Trump’s cabinet and would lead a sprawling agency that safeguards the country’s nuclear arsenal and directs federal research on energy technologies.

Mr. Perry has mounted two failed presidential campaigns, including as a rival to Mr. Trump in the last primaries, before dropping out early. He faced ridicule in 2011 after forgetting, during a debate, that the Energy Department was one of three federal agencies he promised to eliminate were he elected president. Mr. Perry listed the Education and Commerce departments, before drawing a blank on Energy and saying, “Oops.”

A few minutes later Mr. Perry belatedly added, “By the way, that was the Department of Energy I was reaching for a while ago,” but the moment effectively ended his campaign. In 2015 Mr. Trump mocked Mr. Perry for beginning to wear spectacles “so people will think he’s smart,” adding, “It just doesn’t work. You know, people can see through the glasses.”

Mr. Perry, who was governor of Texas for 14 years beginning in 2000, grew up in West Texas and had a long public life in state politics. Before becoming governor, he served as lieutenant governor, agriculture commissioner and spent three terms in the state legislature.

This fall, Mr. Perry competed on “Dancing with the Stars,” the popular U.S. dance competition show that airs on ABC. He and partner Emma Slater were the second of the 13 couples eliminated in the show’s 23rd season.

Trump’s Inner Circle

Rick Perry Age : 66.

: 66. Résumé : Served in U.S. Air Force 1972-1977. Served three terms in Texas House of Representatives beginning in 1984, two terms as commissioner of agriculture starting in 1990, and was elected lieutenant governor in 1998. Became governor in December 2000 when then-Gov. George W. Bush resigned to become U.S. president. Held the office until January 2015. Ran unsuccessfully for president in 2012 and 2016. He was also a contestant on TV show ‘Dancing with the Stars’ in fall of 2016. He and his partner were the second of 13 couples eliminated.

: Served in U.S. Air Force 1972-1977. Served three terms in Texas House of Representatives beginning in 1984, two terms as commissioner of agriculture starting in 1990, and was elected lieutenant governor in 1998. Became governor in December 2000 when then-Gov. George W. Bush resigned to become U.S. president. Held the office until January 2015. Ran unsuccessfully for president in 2012 and 2016. He was also a contestant on TV show ‘Dancing with the Stars’ in fall of 2016. He and his partner were the second of 13 couples eliminated. Notable stand: Claimed credit for Texas’ economic success during his tenure, particularly its job-creation record from 2007 to 2014 while many states still struggled to emerge from recession. Attributed performance to low tax rates and business-friendly regulations.

Mr. Perry has been a reliable backer of GOP energy policies, supporting the Keystone XL pipeline and other priorities of the oil and natural gas industries. Perhaps more than other Republicans, though, he has also shown he backs renewable energy, in particular wind.

In 2005 as governor, Mr. Perry signed legislation that required Texas to dramatically increase its dependence on renewable energy. Along with being the biggest producer of both oil and natural gas, Texas also produces the most wind energy, according to the U.S. Energy Information Administration, the statistical arm of the Energy Department.

Mr. Perry also embraces a common Republican line questioning the scientific consensus that human activity is contributing to climate change. In a debate during his recent presidential run, Mr. Perry said he doesn’t think “the science is settled” on climate change, criticizing “the idea that we would put Americans’ economy at jeopardy based on scientific theory that is not settled yet.”

Mr. Perry’s position on climate change could face renewed scrutiny in light of a memo sent recently by Mr. Trump’s transition team to Energy Department officials. Among other things, the memo asked which staffers have participated in meetings on climate change, raising concerns among some environmental groups that it foretells a shift in the department’s funding and a hunt for staffers who worked on climate change.

Although Mr. Perry has presided over the biggest-energy producing state, much of his focus over the years has been on other issues, including immigration. In an official biography posted on Mr. Perry’s website, he touts his work as governor protecting the border and creating jobs.

The Energy Department was created under President Jimmy Carter following the 1973 oil crisis, but its highest-profile responsibility is overseeing the nation’s nuclear arsenal. One of its agencies, the National Nuclear Security Administration, is tasked with maintaining a safe nuclear stockpile without testing and reducing threat of global nuclear proliferation.

More than half of the Energy Department’s annual budget of around $30 billion goes to protecting the nuclear arsenal and cleaning up nuclear waste and contamination sites around the U.S. The department does oversee areas like the reliability of the electric grid, but the Environmental Protection Agency has been a bigger flashpoint for many hot-button energy issues in recent years.

Energy Secretary Ernest Moniz was pivotal in the Obama administration’s successful efforts to negotiate a deal with Iran curtailing its nuclear program. Mr. Trump has said the deal gives too much to the Iranians, adding that he wants to renegotiate it or do away with it altogether.

Beyond nuclear weapons, Mr. Trump’s new energy secretary will be able to shift the department’s research and development orientation. Under President Barack Obama, the department has focused billions of research dollars on cleaner energy, especially renewables but also technology that lets oil, natural gas and coal burn more cleanly.

The department faced bipartisan criticism early in Mr. Obama’s presidency for awarding a loan guarantee worth $535 million to Solyndra, a solar manufacturer that went bankrupt soon thereafter.

The loan guarantee office is still technically operating, but its activity level has been low partly because of lack of private-sector interest. Mr. Trump isn’t expected to revive the office’s mission, though closing it would likely require action by Congress, which passed legislation during the George W. Bush administration to create the office.

Write to Amy Harder at amy.harder@wsj.com and Michael C. Bender at Mike.Bender@wsj.com