Speaking to a packed news conference in Jerusalem, the Israeli leader said the disease was caught at an early stage and that he will have surgery "over the next few months."
"I will be able to carry out my duties fully before the treatment and within hours afterward," Olmert said. "My doctors ... informed me that there is a full chance of recovery and there is nothing about the tumor which is life-threatening or liable to impair my performance or my ability to carry out the mission which has been bestowed upon me."
"According to what my doctors were told, it is a matter of a microscopic growth, with no metastization which can be removed by a short surgical procedure. According to the medical opinion, there will be no need for radiation treatment or chemotherapy," Olmert said.
Olmert, 62, took office in March 2006 after his predecessor, Ariel Sharon, suffered a debilitating stroke. Olmert delivered the news of his illness calmly, speaking for about three minutes before leaving the room and giving the podium to his doctors.
One of Olmert's doctors, Shlomo Segev, said the prime minister had a biopsy on Oct. 19 and got the results a week later. Another of his doctors, Yaacov Ramon, said Olmert has a "limited growth" that poses no short-term threat.
He said treatment could wait several months without any risk, and that surgery should eliminate the cancer completely. The chances of full recovery are 95 percent, he said.
"The chances for additional treatment like chemo or radiation therapy is next to zero," Ramon said.
He said those who have the surgery are usually hospitalized for three days, followed by a recuperation period at home during which they can work. Foreign Minister Tzipi Livni was expected to take over from Olmert if he is incapacitated by the surgery.
The announcement came at a delicate time in Mideast peacemaking, just weeks ahead of a U.S.-brokered summit designed to relaunch long-stalled peace talks. It was not clear how or if Olmert's illness would affect his already troubled efforts to frame a common outline with the Palestinians ahead of the conference, scheduled to take place in Annapolis, Maryland in either November or December.
Meanwhile, CBS News correspondent Robert Berger reports Israel is taking the heat for reducing fuel supplies to the Hamas-ruled Gaza Strip.
Human rights groups have appealed to Israel's supreme court to stop the reduction of Israeli fuel supplies to Gaza. Prime Minister Ehud Olmert's spokeswoman Miri Eisen says it's a limited measure - retaliation for Palestinian rocket attacks. Palestinians say it is unfair collective punishment.
"The Prime Minister confirmed Israel's commitment that there will not be a humanitarian crisis in Gaza," Eisen said.
In other developments:
No further details were immediately available on Olmert's condition or plans for treatment.
The prostate is a walnut-shaped gland beneath the base of the penis that makes seminal fluid. Prostate cancer is one of the most common forms of cancer. In most men, it grows so slowly that it will never threaten their lives. Treatment often leads to problems having sex or controlling the bladder, so finding a way to distinguish which tumors can safely be left alone is the field's top priority.
The primary risk factor is age, with the disease commonly striking after a man is after 50.
It can be treated with surgery, radiation therapy, hormonal therapy and occasionally chemotherapy, among other treatments.
Leaders in Israel do not issue regular pronouncements on their health, as is the case in some other countries. Health issues were thrust into the fore two years ago when Saron suffered the first of two strokes. The second, hemorrhagic stroke in January 2006 rendered him comatose, and he remains hospitalized in a long-term care facility until this day.
Olmert, who first entered parliament in 1973, was suddenly catapulted into the prime minister's seat after Sharon was incapacitated. Defying initial predictions, he led the new Kadima Party that Sharon had formed to victory in parliamentary elections two months later.
Though widely pilloried for mishandling Israel's war against Hezbollah guerrillas in Lebanon that summer, Olmert used his political talents to keep his coalition government together, surviving in office despite dismal approval ratings.
In recent months, Olmert has been meeting regularly with Abbas in an effort to draft a joint statement on peace ahead of the Annapolis conference. Palestinian President Mahmoud Abbas wants a relatively detailed document outlining a future peace deal, but Olmert prefers a more vague document.
Palestinian negotiator Saeb Erekat sent his best wishes to the Israeli leader.
"We wish him a speedy recovery, and we hope to continue working with him toward achieving a two-state solution and ending the Israeli occupation that began in 1967," he said.
Erekat's boss, President Abbas, is a survivor of prostate cancer.