The plan, which requires congressional approval, calls for closing or abandoning 600 buildings at facilities across the country and gradually reducing the associated workforce by at least 7,200, the Washington Post reported.
Nearly 30,000 people still would be employed in nuclear-arms-related work.
"Today's nuclear weapons complex needs to move from the outdated, Cold War complex into one that is smaller, safer and less expensive," said Thomas P. D'Agostino, administrator of the National Nuclear Security Administration, which runs the weapons program, on Tuesday.
The reductions are an outgrowth of Energy Department studies that began in the mid-1990s. At first, 12 weapons-related sites were reduced to eight.
After the administration signed a nuclear reduction treaty with Moscow in 2003, NNSA officials began looking at how to resize the production complex to match a smaller arsenal, the Post reported. NNSA spends about $800 million each year for security, an amount that it wants to reduce.
D'Agostino also said that Bush approved a new reduction of 15 percent in active U.S. nuclear weapons, which is scheduled to be completed by 2012.
Several independent experts told the Post that roughly 4,600 warheads will remain in the U.S. arsenal, down from about 16,000 at the end of the Cold War and from 10,500 when Bush came into office. President George H.W. Bush eliminated thousands of tactical nuclear weapons, mostly ones placed in Europe and Asia.
While the overall size of the arsenal is classified, NNSA officials confirmed to the Post that only 1,700 to 2,200 of the remaining warheads will be deployed with bombers, missiles and submarines. The remaining active weapons will be kept as spares and for testing with delivery systems.
Bush's decision was made on the recommendation of Secretary of Defense Robert Gates and Secretary of Energy Samuel Bodman with support of the Joint Chiefs of Staff and the Commander of the United States Strategic Command, the White House announced.
Jobs would be cut at the Lawrence Livermore National Laboratory in the Bay Area; the National Nuclear Security Administration's sites near Amarillo, Texas, and in Albuquerque; Los Alamos, N.M.; Oak Ridge, Tenn.; and Aiken, S.C., among others, the Los Angeles Times reported.
Bush's announcement was made days after the House Appropriations Committee slashed funding for a new hydrogen bomb, known as the reliable replacement warhead.
"It's a very sensible thing to do," John Pike, an analyst who directs the security monitoring group GlobalSecurity.org, told Agence France-Presse. "Any nuclear weapon is ... subject to accidental detonation or theft by terrorists."
In reference to the Bush administration, he added: "I think that this is a reasonably easy thing for them to do to look like good guys. ... In terms of America's capacity to incinerate all of our enemies on 15 minutes' notice, this does not alter that."