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Secretaries of homeland security have traditionally been high-profile figures, including former governors and, with Mr. Kelly, a retired Marine Corps general. That isn’t the case with Ms. Nielsen. But administration officials point to her wealth of experience in many issues the agency handles and note that she would be the first secretary to have worked at the agency before.

One downside, though, is she lacks the sort of experience communicating with the public that elected officials have, and that can be important in an emergency or in the case of a terror attack. Acting Secretary Elaine Duke, another nonpolitical homeland expert, ran into trouble for indelicate comments in response to a question about one of the recent hurricanes, for instance.

But Ms. Nielsen is well steeped in the issues that the agency deals with on a daily basis, from her service during the Trump and George W. Bush administrations.

She worked at the Transportation Security Administration and for the White House Homeland Security Council during the Bush years. She then worked in the private sector—at positions including the Center for Cyber and Homeland Security at George Washington University and the National Cybersecurity Center—before being brought into the Trump transition to help guide Mr. Kelly through his Senate confirmation process.

If confirmed by the Senate, she would succeed Ms. Duke, who was deputy secretary under Mr. Kelly and has been acting secretary since July.

DHS, created in the aftermath of the 2001 terrorist attacks, is a sprawling operation with responsibilities including immigration enforcement, disaster response, the Secret Service and U.S. border and airport security.

As such, Ms. Nielsen would be thrust to the forefront of some of the administration’s most controversial initiatives. Those include Mr. Trump’s effort to build a wall on the southwest border with Mexico, increase deportations of undocumented immigrants, enforce travel restrictions on people from targeted countries, and increase vetting of travelers to the U.S. She would also take over the Federal Emergency Management Agency at a time of intense recovery efforts following a series of damaging hurricanes.

Her White House experience may be an asset in dealing with much of that, said David Heyman, a senior DHS official in the Obama administration who occasionally has worked with Ms. Nielsen.

“There needs to be a very tight relationship between DHS and the White House,” he said. “Kristjen provides that seamless bond, as well as deep knowledge and experience in homeland security to address these critical issues.”

At the White House, Ms. Nielsen was exposed to issues across the administration and also helped Mr. Kelly work to gain control over an unwieldy West Wing operation.

Senate confirmation hearings for Ms. Nielsen are likely to serve as a forum for debate over Mr. Trump’s immigration agenda. But unlike other possible choices, Ms. Nielsen doesn’t arrive with a long history of controversial personal statements about hot-button issues, which may smooth her pathway.

Several administration officials emphasized Ms. Nielsen’s deep familiarity with the issues that DHS handles. She also now has three months of experience at the upper levels of the White House, where she was exposed to issues across the administration and helped Mr. Kelly work to gain control over an unwieldy West Wing operation.

Among those also considered for the job was Rep. Michael McCaul (R., Texas), chairman of the House Homeland Security Committee, according to people familiar with the process.

The news of Ms. Nielsen’s coming nomination was earlier reported by Politico.