Bush is expected to name an acting director soon.
The NNSA, an energy department agency, is responsible for maintaining the US nuclear weapons stockpile and reducing the global threat posed by weapons of mass destruction.
It was established 2000 after the Wen Ho Lee espionage scandal at the Los Alamos lab in New Mexico, birthplace of the atomic bomb and the site of US nuclear weapons research.
A Taiwanese-American scientist, Lee was accused of stealing secrets about the US nuclear arsenal for China in December 1999.
The charges were later dropped but Lee pleaded guilty to improperly handling of sensitive data.
Brooks' departure followed two other incidents at the lab.
Last June, a security breach at Los Alamos reportedly led to the theft of files containing personal information on more than 1,000 workers.
The breach had gone unreported for months.
In October, a drug raid on a Los Alamos trailer park turned up secret data taken from the lab by a female employee.
The discovery raised concerns that the woman might have tried to sell the information to support a drug habit.