The Times report cites two sources briefed on the matter.
Brand will leave her position 'in the coming weeks, ' the statement said.
Brand attracted interest because of her potential to assume a key role in the Trump-Russia investigation.
Last week, Brand headed up an all-day summit on human trafficking at the Justice Department where she told a packed room that "combatting this evil is one of our top priorities at the Justice Department". In addition to her third in command position she's now vacating, Rachel worked in the Office of Legal policy at the DOJ under the second Bush administration and then served on the Privacy and Civil Liberties Oversight Board under the Obama administration.
"I think it's a disgrace what's happening in our country", Trump said last week when he was asked about the release of a memo from Republicans on the House Intelligence Committee claiming abuses in the Russian Federation investigation.
Qualcomm dismisses Broadcom's latest offer - claims it still undervalues the company
Broadcom said it "welcomes" the move in an official response this morning and expressed a willingness to sweeten the deal. Qualcomm shareholders will have their say on March 6 when they choose between Broadcom's slate and the existing board.
After just nine months on the job, Brand had grown increasingly uncomfortable with Trump's escalating attacks on the Justice Department and the Federal Bureau of Investigation, which she and other law enforcement professionals feared was beginning to undermine the rule of law, according to sources familiar with her thinking.
Rosenstein is the only official with legal authority to fire Mueller, and it is widely believed he would resign if ordered to do so without good cause.
Brand previously worked in the administrations of both Presidents George W. Bush and Barack Obama as the head of the Justice Department's office of legal policy and as a member of an oversight board for privacy and civil liberties. Attorney General Jeff Sessions, himself repeatedly criticised by Trump, praised her "critical role in helping us accomplish our goals as a department". His broadsides have strained morale at the institution known for its vaunted independence from the White House.
Brand recently pushed Congress to renew a foreign intelligence surveillance program that gives the USA government authority to spy on foreigners located outside the country. The measure passed, and Trump signed it into law in January. In her current capacity, she oversaw a number of politically challenging areas of the department, including the civil rights, antitrust and civil divisions.
A Justice Department official said that Jesse Panuccio, the Principal Deputy Associate Attorney General, will temporarily take over Brand's job until a replacement is named.