Lt. Gen. Colin L. Powell, heir apparent to the high-turnover post of national security adviser to President Reagan, has proved unusually popular in an administration often known for feuds and backbiting.

Powell, who has served as No. 2 to Frank C. Carlucci on the National Security Council staff for the last 10 months, would be the first black to hold the job and Reagan's sixth national security adviser. Administration officials said he will be appointed formally in the Rose Garden today, when the president plans to accept the resignation of Defense Secretary Caspar W. Weinberger and nominate Carlucci to succeed him.

Powell, 50, once served as Weinberger's top military aide and commanded the U.S. Army's 5th Corps in West Germany before becoming Carlucci's deputy. According to several Army colleagues, his acceptance of a series of essentially political appointments derailed a military career that might have made him the Army's first black chief of staff. Powell resisted promotion to the No. 2 national security adviser's job, he has told friends, and became Carlucci's deputy only after Reagan asked him to take the job.

"He always does what he says he is going to do," said a senior White House official who has worked closely with Powell. The official said that Powell was Carlucci's choice as his successor and was supported by Secretary of State George P. Shultz.

Despite Powell's popularity and military experience, it appears that his work is cut out for him in his new job. Powell lacks the broad experience of Carlucci and does not have a long, personal relationship with the president, qualities usually associated with success in the Reagan administration.

Until Carlucci took over last Jan. 2, the national security adviser's position had been a trouble spot of the Reagan presidency. Reagan's fourth national security adviser, Vice Adm. John M. Poindexter, was a principal in the covert attempt to swap U.S. arms to Iran in exchange for American hostages being held in Lebanon. Poindexter testified at a congressional investigation that he never told Reagan about the illegal diversion of some of the proceeds to aid the Nicaraguan contras.

As military aide to Weinberger, who opposed the swap, Powell was one of five men in the Pentagon who knew that arms were being transferred to the Central Intelligence Agency to be sent to Iran. A House Armed Services Committee report said Powell sent a memo to the White House asking about the legal requirement to notify Congress of the arms transfer but heard nothing back from Poindexter.

Much of the effort of Carlucci and Powell during the past year has been directed at attempting to restore the reputation and morale of the discredited National Security Council staff and establish a sense of teamwork in the Reagan White House.

As deputy director of the NSC, Powell headed the Policy Review Group, an interagency body that responded to criticisms of NSC staff covert activity and secrecy by giving high-level officials at the Pentagon, State Department and CIA greater opportunity to make their views known.

"Like Frank, I am a great believer that the interagency process works best when everybody has a chance to say his piece and get his positions out on the table . . . that when we forward the final decision package to the president or present it to him orally, everybody who played knows he has been properly represented and had his day in court," Powell said in an interview last March.

Coworkers interviewed yesterday praised Powell for having "a keen intellect" and "pragmatic sense of purpose." One colleague called him a "strong man with a gentle disposition who has exhibited qualities of trust and good sense that were sorely needed at the NSC."

He is similarly valued by former Pentagon colleagues. "He's not a guy who's come up as a Pentagon lounge lizard," an Army official said. "He's got a lot of field time."

Top-ranking Army officials described Powell as "a soldier's soldier" who is "extradordinarily well-respected."

According to Defense Department officials, Powell had the confidence of Weinberger and the Joint Chiefs of Staff, which gave him a major role in military operations, including the 1986 raid on Libya. In the White House he joined Carlucci in advocating a strong U.S. role in the Persian Gulf, advocacy that led to the controversial decision to reflag Kuwaiti oil tankers and deploy an American armada in the region.

Appearing on the "McNeil/Lehrer Newshour" on June 16, Powell defended U.S. actions in the gulf as necessary to protect freedom of navigation and to deny the Soviets "any greater influence in the region."

Powell, the son of immigrant parents from Jamaica, was born in New York City and attended the City College of New York. He was commissioned a second lieutenant when he finished college in 1958 and rose rapidly in rank. He won a Purple Heart in Vietnam in 1963, when he fell into a trap near the Laotian border, and his foot was pierced by a sharpened stick.

White House officials said that at Carlucci's urging Powell has briefed the president more frequently than past deputy national security advisers, giving him what an aide called "a flying start" at establishing his own relationship with Reagan. They also predicted that the departure of Weinberger would ease friction in high-level councils of the administration and make the national security adviser's job less difficult than in the past.

"The policy of this administration is well in place, and what's important now is that we pull together as a team," a White House official said. "Colin excels at that. He is a genuine honest broker, who will see that everyone has his say."

Staff writer Molly Moore contributed to this report.