Moving quickly to fill a critical White House vacancy, President Trump named Army Lt. Gen. H.R. McMaster as national security adviser Monday, one week after ousting Michael Flynn.

Mr. Trump has favored military men for top security and anti-terrorism roles in the administration and turned to a career soldier with a reputation as a cutting-edge strategist for his closest security and foreign policy adviser, the one who controls the flow of information from the national security bureaucracy to Mr. Trump’s desk.

Mr. McMaster, 54, has been serving as director of the Army Capabilities Integration Center and deputy commanding general of futures at the U.S. Army Training and Doctrine Command.

“He is man of tremendous talent and tremendous experience,” Mr. Trump said when announcing the appointment at his Mar-a-Lago Club in Florida before returning to Washington. “I’ve watched and read a lot over the last days. He is highly respected by everyone in the military, and we are very honored to have him.”

In 2014, Time magazine named Mr. McMaster as one of its 100 most influential people in the world, saying he “might be the 21st century Army’s pre-eminent warrior-thinker.”

The president moved quickly to find a replacement for Mr. Flynn, a retired Army lieutenant general who was forced to resign after misleading Vice President Mike Pence about phone conversations he had with Russia’s ambassador to Washington during the presidential transition period.

The White House said there had been an “erosion of trust” with Mr. Flynn. During a visit to Brussels on Monday, Mr. Pence said he was disappointed that Mr. Flynn had not been candid with him.

Mr. McMaster joined Mr. Trump for the announcement at Mar-a-Lago, where the president spent the holiday weekend.

In brief remarks, Mr. McMaster said he was grateful for the opportunity to continue to serve the country.

“I look forward to being on the national security team and doing everything I can to advance and protect the interests of the American people,” he said.

Mr. Trump interviewed several candidates for the job over the weekend, including at least three generals and John R. Bolton, former ambassador to the United Nations.

Mr. Bolton also was under consideration for secretary of state, but that job went to Rex W. Tillerson, a former Exxon Mobil Corp. CEO.

Mr. Trump said he still wanted to find a place in the administration for Mr. Bolton, whose foreign policy views are more hawkish that those espoused by the president.

“John Bolton we are going to ask to be working with us in a somewhat different capacity,” he told reporters at Mar-a-Lago. “John is a terrific guy. We had some really good meetings with him. He knows a lot — a good number of ideas that I must tell you I agree with.”

Mr. McMaster wasn’t Mr. Trump’s first pick for a replacement to head the National Security Council.

Vice Adm. Robert Harward turned down the post Thursday, citing “family considerations” and difficulties overcoming financial entanglements from his job with defense contractor Lockheed Martin Corp., a senior administration official said.

Adm. Harward, who is close to Defense Secretary James Mattis, was in negotiations with the White House over bringing some of his own staff to the embattled National Security Council. Reuters reported that Mr. Trump had told Mr. Flynn’s deputy, K.T. McFarland, that she could stay.

The president gave Mr. McMaster “full authority” to “hire whatever staff he sees fit,” said White House deputy press secretary Sarah Huckabee Sanders.

On Monday, that power was cheered by Mr. McMaster’s predecessor in the Obama White House — Susan E. Rice, who publicly urged him to get rid of a national security wing led by presidential strategist Stephen K. Bannon.

“Hope you will be able to choose your team, have direct reporting and daily access to POTUS, and can eliminate Strategic Initiatives Group,” Ms. Rice wrote in a congratulatory note to Mr. McMaster on Twitter.

The Strategic Initiatives Group is a layer of the White House National Security Council that is led by Mr. Bannon.

Michael McFaul, a former U.S. ambassador to Russia and early critic of the Trump administration, issued a similar warning while saying he has admired Mr. McMaster since they worked together at the Hoover Institution think tank in 2001.

“I have a lot of respect for HR,” Mr. McFaul wrote on Twitter. “HR will not roll over and salute Bannon.”

The selection of Mr. McMaster was cheered on Capitol Hill.

Sen. John McCain, Arizona Republican and chairman of the Senate Armed Services Committee, called Mr. McMaster “an outstanding choice.”

“I have had the honor of knowing him for many years, and he is a man of genuine intellect, character and ability. He knows how to succeed,” said Mr. McCain, a frequent critic of Mr. Trump. “I give President Trump great credit for this decision, as well as his national security Cabinet choices. I could not imagine a better, more capable national security team than the one we have right now.”

Sen. Tom Cotton, an Arkansas Republican on the Senate Armed Services Committee and the Select Committee on Intelligence, said Mr. McMaster was “one of the finest combat leaders of our generation and also a great strategic mind. He is a true warrior scholar.”

Mr. Trump also announced that retired Army Lt. Gen. Keith Kellogg, who was acting national security adviser for a week, would stay on as chief of staff for the council. He said the two generals knew each other well and would make a good team.

“I think that combination is something very, very special,” the president said.

Mr. McMaster is perhaps best known for his 1997 book, “Dereliction of Duty,” which faulted the White House and the top military officers of the day for strategic and tactical failures during the Vietnam War.

“The war in Vietnam was not lost in the field, nor was it lost on the front pages of The New York Times or the college campuses. It was lost in Washington, D.C.,” he wrote in the book.

Mr. Pence’s remarks on Mr. Flynn’s resignation was the first time he spoke publicly about the issue.

“I was disappointed to learn that the facts conveyed to me by Gen. Flynn were inaccurate,” he said at a press conference in Belgium with NATO’s secretary general. “I’m very grateful for the close working relationship I have with the president.”

Mr. Pence went on TV news programs and, based on assurances from Mr. Flynn, vouched that Mr. Flynn had not discussed U.S. sanctions against Russia with the ambassador. Mr. Flynn’s claims were contradicted in news reports based on leaked information from the intelligence community.

Mr. Trump fired Mr. Flynn last week, saying he had lost trust in him.

In Belgium, Mr. Pence said the president’s decision to ask for Mr. Flynn’s resignation was proper.

“We honor Gen. Flynn’s long service to the United States of America, and I fully support the president’s decision,” the vice president said. “It was handled properly and in a timely way. I have great confidence in the national security team of this administration going forward.”

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