The Devin Nunes memo put out by House Republicans last week was seen as a possible pretext for Trump to get rid of Rosenstein, which would leave Brand in charge - a possibility that has seemed to appeal to Trump in the past.
The New York Times first reported her resignation Friday afternoon. She is expected to take a job as general counsel in the private sector.
Brand, who became associate attorney general in May, has kept a relatively low profile and, unlike other top officials, has not been personally targeted by Trump. A source said she was going to work as an executive at retailer Walmart.
Rachel Brand, nominee to be Associate Attorney General, testifies before the Senate Judiciary Committee on Capitol Hill in Washington March 7, 2017.
Brand was also a high-ranking official in the department under George W. Bush.
"Thank you, Rachel, for your kind words and, more importantly, for your strong leadership as our third in command at the department", Sessions said.
Toys 'R' Us Going-Out-Of-Business Sales Could Start Today
Matthews and the Outlet Shoppes of the Bluegrass in Simpsonville are among the stores that will be closing. LEGO also announced it was having trouble with sales and cut 1,400 jobs.
Firing Rosenstein would be a colossal move by Trump.
The daughter and granddaughter of Dutch dairy farmers in Iowa, Brand has been praised for her deep knowledge of the Justice Department. She was in line to oversee the investigation if Rosenstein stepped down.
The attacks have escalated as Republicans in Congress criticised the handling by the Justice Department, FBI and Federal Intelligence Surveillance Court of warrants for surveillance of a Trump campaign adviser, Carter Page, who had ties to Russian Federation.
"She felt this was an opportunity she couldn't turn down", Gorelick told the Associated Press. She has held politically appointed positions in the past three presidential administrations.
In the position, she oversaw the department's efforts on civil and civil rights matters as well as the antitrust, tax and environment and natural resources divisions. Andrew McCabe, the former deputy director of the FBI who received some of the fiercest of Trump's attacks, was reportedly pushed out of the bureau last week. The memo alleged the Federal Bureau of Investigation abused its power regarding surveillance methods, and said Rosenstein signed off on at least one FISA application of former Trump campaign aide Carter Page.