Doctors said they expect Mueller to make a full recovery.
Mr. Bush and Attorney General John Ashcroft knew of Mueller's condition when he was chosen for the job, officials said.
Mr. Bush was convinced it was caught early and would not hinder Mueller's ability to serve as FBI director, senior White House officials said.
The news became public Friday in papers Mueller submitted to senators who will consider his nomination.
Dr. Peter Carroll, a prostate cancer specialist in San Francisco who will perform Mueller's surgery, said Mueller's prostate and the tissue surrounding it will be removed and that should take care of the cancer.
"It should not in any way impact his ability to do the job," said Carroll in an interview. "He is in excellent physical condition."
There is no evidence the cancer has spread and a 90 percent chance it will not reappear, he said.
Mueller is not expected to have radiation or chemotherapy treatment.
"It's very limited and localized," said Mindy Tucker, Justice Department spokeswoman. "There's not a concern about him being able to do the job."
Mueller, 56, a veteran prosecutor who is currently U.S. Attorney in San Francisco, could not be immediately reached for comment.
Mueller was tapped by the Bush administration to repair the FBI following a string of embarrassments ranging from bungled Oklahoma City bombing documents to the discovery of an FBI spy.
Prostate cancer is one of the most common forms of cancer and has affected many other officials including former presidential candidate Bob Dole and New York Mayor Rudolph Giuliani.
There were 2.8 million reported cases of prostate cancer in the United States in 1996, according to the latest figures available from the National Center for Health Statistics. About 192,000 men had surgery to treat the cancer.
About 3 percent of men with prostate cancer die of it. In 1998, 32,203 died of the cancer, according to NCHS.
Mueller had a blood test for prostate cancer last September that turned up positive. He had another one in October, also positive, and had a biopsy in Washington that showed a small amount of cancer, said Carroll.
He had another evaluation in San Francisco in April. Carroll said Mueller has a small tumor on his prostate, which is a walnut-shaped organ located below the bladder.
Mueller will be in the hospital for two to three days following the two-hour surgery. The exact date of the operation, which will be performed in San Francisco, has not yet been scheduled.
Most men can return to their full schedule within 2 to 6 weeks after surgery, said Carroll. Because Mueller is in good shape, he is expected to go back to work quickly.
Senate Judiciary Chairman Patrick Leahy, D-Vt., "doubts this will be a factor in the confirmation process. Mr. Mueller's overal health seems excellent," spokesman David Carle said.
Mueller was evaluated at a cancer center at the University of California in San Francisco on April 17, according to a letter from Carroll, head of the urology department.
The letter was made available Friday by the Senate Judiciary Committee.
Mueller submitted a questionnaire of personal information to the committee as part of the confirmation process. Asked about the state of his health, Mueller said it was "generally excellent," but referred to Carroll's letter.
"Mr. Mueller had been diagnosed with a very localized prostate cancer," said Carroll. "This diagnoses was confirmed here."
"He is an excellent candidate for a variety of different treatment options and has a very, very high likelihood of cure with any," said Carroll.
Carroll said he did not believe that Mueller's diagnosis and treatment "will, in any way, impact on his ability to function and carry on his responsibilities normally."
Mueller, a decorated Vietnam veteran, was chosen by Mr. Bush to fill a 10-year term as the sixth full-time director of the FBI.
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