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The Trump administration ordered the change in a memorandum signed recently by White House national security adviser Robert O’Brien, the officials said Friday.

The decision drew criticism from some former senior defense officials and lawmakers concerned that it would further weaken a key alliance and empower U.S. adversaries. Moscow is likely to welcome the open display of differences between two key North Atlantic Treaty Organization allies, U.S. experts said, though Russia didn’t comment publicly on the development.

One senior U.S. official said that the administration has been discussing the move since September and that it isn’t linked to German Chancellor Angela Merkel’s decision not to attend a G-7 meeting Mr. Trump was to host in Washington at the end of June.

But the official acknowledged that it reflected the Trump administration’s long frustration with German policy, especially the nation’s level of military spending and its insistence on completing the controversial Nord Stream 2 pipeline that will channel Russian gas directly to Germany under the Baltic Sea.

A senior German defense official said his government hasn’t been formally notified of the move, though it had been hearing rumors through diplomatic channels that U.S. troop reductions were coming.

“We always knew Trump would lash out when he is under pressure domestically, but we thought he would first pull out of Afghanistan,” the official said. “This move will not help friends of the U.S. in Germany who are working hard to preserve the trans-Atlantic relationship, but it will boost the anti-American sentiment that has been spreading here.”

Germany’s defense minister promised last year to meet the NATO goal of spending 2% of its GDP on defense, but the target date for reaching that objective is 2031.

Pentagon officials declined to comment.

Richard Grenell, the former ambassador to Germany who recently stepped down as the acting director of national intelligence, has long pressed for a significant troop cut, though the administration wasn’t of one mind on the question and some other officials hoped for a more modest reduction.

As part of the decision, the Trump administration is also rethinking the number of U.S. troops sent to Germany on a temporary basis for training, the officials said.

Germany has long been a major hub for U.S. military training in Europe, and an array of important American military bases are located there. They include major military training ranges at Grafenwoehr and Hohenfels, as well as the headquarters for the U.S. Air Force and Army forces in Europe. The U.S. Africa Command also is located in Germany.

The Pentagon embraced a defense strategy in 2018 that calls for stepping up efforts to deter possible Russian and Chinese aggression. As he has campaigned for reelection, Mr. Trump has urged returning troops from what he has called the “endless wars” in Afghanistan and the Middle East.

Critics say that in pushing to reduce the U.S. military presence in Germany, Mr. Trump appears to be hamstringing his own military strategy.

Frederick Hodges, a retired Army general who previously commanded U.S. Army forces in Europe, said the U.S. presence in Germany has facilitated the Pentagon’s ability to project power in Europe and beyond.

“Russia has done nothing to lower its threat to our allies. Why would we want to reward that behavior with a reduction of our forces in Europe?” Gen. Hodges said. “Germany is the most important ally we have in Europe. This looks like punishment somehow.”

Mr. Trump’s order would give the Pentagon some flexibility in carrying out cuts as long as there were no more than 25,000 troops in Germany at any period, a person familiar with the plan said.

Some American officials suggested that the U.S. might meet that ceiling and still maintain a significant force in Europe by shifting some of the troops to Poland and other European nations while bringing the rest home.

One official said that more than 1,000 of the troops leaving Germany would be deployed to Poland, which is meeting the NATO military-spending goal and has decided to stop buying Russian gas altogether after 2022.

The infrastructure in Poland and other Central European countries, however, generally isn’t as well developed as in Germany. And the suddenness of the move might concern allies, including South Korea, which is locked in a dispute with Washington over how much it should pay to defray the cost of the U.S. military deployment there.

“A move like this not only erodes trust with Germany but with other allies, too,” said James Townsend, a former senior Pentagon official for Europe and NATO. “Other allies will be asking, ‘Will I be next?”

Congress has yet to be officially informed of the decision. Sen. Jack Reed (D., R.I.), the senior Democrat on the Senate Armed Services Committee, criticized it as a “favor to Putin and another leadership failure by this administration that further strains relations with our allies.”

The Quincy Institute, a think tank that favors a limited role for the American military, praised Mr. Trump’s decision, urging that the administration follow it with a broader strategy that “empowers Europe to take responsibility for its own security.”

The Trump administration has taken other actions that have proved controversial regarding U.S. defense in Europe.

In May, Rep. Eliot Engel (D., N.Y.), who chairs the House Foreign Affairs Committee, and other lawmakers complained that the Pentagon was taking funds from military construction efforts in Europe to pay for the border wall with Mexico. The cuts involved $274 million in spending that had been intended to construct sites to store munitions, fuel and other logistical requirements.

—Alan Cullison and Bojan Pancevski contributed to this article.