Mr. Murphy said Peter G. Verniero, a former justice on the New Jersey Supreme Court who now works for a law firm, will oversee the investigation. The governor said he planned to speak with Ms. Brennan later on Monday.

Reports of Ms. Brennan’s allegation of sexual assault surfaced last week, but Ms. Brennan made her accusations public in an article in The Wall Street Journal published online on Sunday. After the article’s publication, Ms. Brennan released a statement in which she criticized Mr. Murphy’s administration.

“Several senior level members of the Murphy administration were aware of my assault and failed to take meaningful action,” said Ms. Brennan, the chief of staff at the New Jersey Housing and Mortgage Finance Agency. She called the actions of several members of Mr. Murphy’s staff “unacceptable.”

In response, Mr. Murphy and his wife, Tammy, issued their own lengthy statement, saying that they believed the administration had handled the accusations appropriately. But they also said that his transition team had made a mistake in hiring Mr. Alvarez, who recently abruptly resigned as the chief of staff at the Schools Development Authority, which deals with school construction.

“I wish we hadn’t made the hire in transition, period,” Mr. Murphy told reporters. “I’m sick to my stomach once I heard what happened.”

The governor maintained that he had not been aware of Ms. Brennan’s allegation until Oct. 2, when The Wall Street Journal provided information about its findings to his office. But Mr. Murphy said that he believed his administration had handled the allegation appropriately once it was brought to the attention of his chief counsel, Matt Platkin, in March.

“These processes, within government at least, are confidential and treated confidentially,” Mr. Murphy said. “And that’s for a reason, to make sure that there’s a fairness associated with it. That you’re not, even inadvertently, putting your hand on the scale. I believe in this case it obviously was followed because we did not hear about it until October 2nd.”