Some of Brown's critics agreed with his decision, saying it would put the focus on efforts to manage the aftermath of the disaster, including helping the thousands of people left homeless.
Brown took a political bullet for the White House with his resignation announcement, CBS News Correspondent Jim Stewart reports.
Mr. Bush named R. David Paulison, head of the FEMA's emergency preparedness force, to replace Brown.
The president was told of Brown's resignation earlier Monday and spoke to Homeland Security Secretary Mike Chertoff, who was Brown's boss, from Air Force One in the afternoon as he flew back to Washington from an overnight visit to the region.
White House spokesman Scott McClellan said the White House did not seek Brown's resignation.
"This was Mike Brown's decision and we respect his decision," McClellan said.
McClellan praised Brown's work but conspicuously left out any reference to his contribution to the Katrina efforts.
"The president appreciates Mike Brown's service," he said. "Mike has done a lot of great work on a number of hurricanes."
Besides leading FEMA's emergency preparedness force, Paulison has led the U.S. Fire Administration since December 2001, according to a biography posted on FEMA's Web site.
He is a career firefighter from Miami who was among the emergency workers responding to Hurricane Andrew in 1992 and the crash of ValuJet Flight 592 in the Florida Everglades in 1996.
Paulison also was chief of the Miami-Dade Fire Rescue Department, leading 1,900 personnel and a $200 million operating budget. He was in charge of Dade County's emergency management office, according to the biography.
Paulison was also in the news in 2003 for suggesting keeping duct tape to prepare for a terror attacks.
In an interview, Brown said he feared he had become a distraction.
His resignation came three days after he was sent back to headquarters from the Gulf area, where he had been the government's disaster point-man. It also came a little more than a week after Mr. Bush, on his first on-the-ground visit to the region after the storm, said, "Brownie, you're doing a heckuva job."
"The focus has got to be on FEMA, what the people are trying to do down there," Brown told The Associated Press on Monday.
Brown said he spoke Saturday to White House chief of staff Andrew Card and was not asked to resign. Brown said the decision to step down was his.
"I think it's in the best interest of the agency and the best interest of the president to do that and get the media focused on the good things that are going on, instead of me," he said.
Brown said he last talked to Mr. Bush five or six days ago.