Olmert said he would not run in his party's primary election Sept. 17 and would step down afterward to allow his successor to form a government. But because of Israel's political system, he could serve until well into next year.
His decision will end a long public career that has been clouded by allegations of corruption that have battered him in recent months.
Olmert's popularity dropped below 20 percent at one point after his bloody but inconclusive war in Lebanon in 2006.
Political analysts had been predicting his resignation for weeks as details of the latest allegations against him dominated the news.
The most damaging inquiry focuses on Morris Talansky, a 76-year-old American Jewish businessman who testified that he handed envelopes stuffed with tens of thousands of dollars to Olmert before he became prime minister, in part financing a luxurious lifestyle of expensive hotels and fat cigars.
Talansky gave lengthy public testimony for days in a Jerusalem courtroom, defending his allegations under cross-examination by Olmert's attorneys - although Olmert has never been formally charged with a crime.
The latest allegation was that Olmert double and triple-billed trips abroad to Jewish institutions, pocketing the difference or financing trips for relatives. Other allegations include a shady real estate deal and questionable political appointments - all before he became premier.
Olmert's brief address from his official Jerusalem residence included harsh criticism of the police investigations. He said he was choosing the public good over personal justice. Although he has consistently denied wrongdoing, he had pledged to resign if indicted.
"I was forced to defend myself against relentless attacks from self-appointed 'fighters for justice' who sought to depose me from my position, when the ends sanctified all the means," Olmert said, appearing angry and reading from a text.
He did not answer questions from reporters gathered in his courtyard.
His decision not to run in the Kadima primary sets in motion a process to choose a new prime minister. Main candidates in his party are Foreign Minister Tzipi Livni and Transport Minister Shaul Mofaz, a former defense minister and military chief of staff.
Polls show Livni with an advantage in the primary. If she were to replace Olmert, she would become the second female prime minister in Israeli history, after Golda Meir.
If Olmert's successor as party leader can form a coalition, Israel could have a new government in October. If not, an election campaign could extend into 2009. Olmert would remain in office until a new premier is chosen, heading a caretaker government after he submits his resignation to President Shimon Peres.
Israel's labyrinthine political system is weighted against a quick internal Kadima resolution to the crisis - with hard-line ex-premier Benjamin Netanyahu of Likud waiting to take advantage.
Netanyahu opposes most concessions to the Palestinians and Syrians suggested by Olmert.
Olmert's Kadima Party has only 29 seats in the 120-member parliament, and his successor must patch together a coalition with a majority. Olmert's main partner, Labor, is headed by another ex-premier, Ehud Barak, who would like his old job back and may be more comfortable forcing an election than playing second fiddle to Livni.
Barak, currently Israel's defense minister, supported Olmert's decision and left open the possibility that he might seek to replace him.
"We will assist every opportunity to move forward," Barack said during a visit to the United Nations.
The ultra-Orthodox Shas, another member of Olmert's coalition, traditionally exacts a huge price in budgets for its constituency, as well as pledges of legislation, before it joins a government.
Its participation in a new Kadima team is not guaranteed.
Possibly hinting at his expectation of being in power for some time, Olmert pledged to work for peace "as long as I am in my position," and said talks with Palestinians and Syria are "closer than ever" to achieving understandings.
But the internal turmoil could make it difficult for Olmert to close deals with either the Palestinians or Syria, agreements that long have eluded Israeli leaders.
Palestinian Foreign Minister Riad Malki said Olmert's decision would not change much. "It's true that Olmert was enthusiastic about the peace process, and he spoke about this process with great attention, but this process has not achieved any progress or breakthrough," Malki said. He said the Palestinians would deal with any Israeli government.
Olmert spoke as his delegation to indirect talks with Syria returned from a fourth round in Turkey. The two sides set another round for August.
Israeli political analyst Yossi Alpher said Olmert's resignation would at least slow the process. "The Arabs are asking themselves how useful an agreement with Olmert would be, because he is a self-proclaimed lame duck and he will have a hard time to get his deals approved," Alpher said.
While neither the Palestinians nor Syria would be eager to close a deal with a lame-duck leader, the prospect of Netanyahu lurking in the wings could propel them forward despite the fluid political situation.
White House spokesman Gordon Johndroe said President Bush called Olmert to pledge continued cooperation.
"Relations between the United States and Israel during Prime Minister Olmert's tenure have been exceptionally close and cooperative, and the president has appreciated his friendship, his leadership, and his work for peace," Johndroe said. "We're confident that the close United States-Israel relationship will continue in the future."
Israeli political analyst Dan Margalit, a longtime friend of Olmert who recently fell from his favor, called the decision to step down "a sad end to a miserable career."
Olmert took over as premier after Ariel Sharon suffered a massive stroke in January 2006. Olmert was a relatively obscure politician who had been named vice premier as a move of political expediency when it appeared that Sharon would serve indefinitely.
Instead, Olmert, known as a backslapping political operator with charm and fluent English, suddenly became prime minister.
His first initiative was to go where even the popular Sharon never dared - following up Sharon's unilateral 2005 withdrawal from Gaza with a plan for a similar pullback in the West Bank.
But events soon overtook him. Hezbollah guerrillas in Lebanon staged a cross-border raid, killing three Israeli soldiers and capturing two. Olmert hastily ordered his military into battle, pledging to smash Hezbollah and bring back the soldiers, but accomplishing neither goal.
Instead, Hezbollah rained nearly 4,000 rockets on Israel, and Israeli forces ran an operation, later roundly criticized, that depended on airstrikes and bombing and only later on sweeps by ground forces.
The war ended with a U.N. Security Council resolution that allowed both sides, equally battered, to declare victory, but an Israeli commission of inquiry excoriated Olmert and his team for the handling of the war.
Olmert's proposed West Bank pullback dropped off the table as his popularity plunged.
Like Sharon, Olmert underwent a political transformation from hawk to moderate, from backing Israeli control of all of the West Bank and Gaza Strip with constant settlement expansion to helping Sharon lead Israel's unilateral withdrawal from Gaza.
Olmert, 62, gained governing experience in a decade as mayor of Jerusalem, balancing Jewish and Palestinian interests and wrestling with constant budget shortfalls by raising money abroad.
Bitterly summing up during his 10-minute address Wednesday, Olmert said, "Did I make mistakes over my political career?
Without a doubt, yes, and I regret them and I am sorry. But is the real picture that which is presented to the public? Absolutely not."
(Copyright 2008 by The Associated Press. All Rights Reserved.) AP-NY-07-30-08 1838EDT
