Efforts to reach Ms. Bachelet in Chile were not immediately successful.

The change comes as the Trump administration has taken an increasingly dim view of human rights diplomacy at the United Nations. The administration withdrew from the Human Rights Council in June, partly over the frequent criticism of Israel and other actions that the administration described as two-faced.

After Mr. al-Hussein’s office criticized the White House over the practice of separating children from parents to deter undocumented immigrants, Nikki R. Haley, the American ambassador, angrily accused it of ignorance and hypocrisy.

Ms. Haley had a measured reaction to the choice of Ms. Bachelet.

“The failures of the Human Rights Council make the Secretary-General’s selection of a new High Commissioner for Human Rights all the more important,” she said in a statement. “It is incumbent on the Secretary-General’s choice, Ms. Bachelet, to avoid the failures of the past.”

Human rights advocates welcomed the choice of Ms. Bachelet.

“As a victim herself, she brings a unique perspective to the role on the importance of a vigorous defense of human rights,” Kenneth Roth, the executive director of Human Rights Watch, said in a statement. “People worldwide will depend on her to be a public and forceful champion, especially where offenders are powerful.”

Ms. Bachelet became involved in Chilean human rights activism practically at the onset of Gen. Augusto Pinochet’s dictatorship in September 1973. She was studying medicine at the University of Chile and active in the Socialist party when a military coup toppled the government of Salvador Allende.