"I have decided to end my functions as prime minister of the government of Israel," Olmert said in remarks broadcast on Israeli television.
"I hope that Tzipi Livni will succeed in forming a national government with the composition she wants... For my part, I will help her with all my strength."
"It has certainly been a very long goodbye ... but Olmert could be hanging around for a few months yet," David Chater, Al Jazeera's correspondent in Jerusalem, said.
|Eli Yishai, leader of the Shas party, has threatened to leave the coalition [ EPA]
After her win in the Kadima party leadership vote, Livni now has the task of forming a coalition government in order to prevent snap general elections.
Polls have indicated that such a vote would sweep the opposition Likud party to power.
Should Livni succeed in forming a coalition, she would become the first female prime minister in Israel for 30 years.
Olmert was criticised for his handling of the 2006 war in Lebanon against Hezbollah, which ended without a decisive Israeli blow against the Shia Muslim organisation.
He is also facing several allegations of corruption, with police investigating claims that he accepted cash payments from an American businessman before he became prime minister.
Olmert had said on July 30 that he would step down once a new leader was chosen by the Kadima party.
His resignation comes amid flagging peace talks between Israel and the Palestinians, which by the end of this year were intended to lead towards an agreement on the formation of a Palestinian state.
Although Livni has led the negotiations on the Israeli side, the two sides remain divided over final borders, Jewish settlements in the West Bank, the future status of Jerusalem and the fate of about 4.6 million Palestinian refugees.
Complicating Livni's attempt to form a coalition, the ultra-Orthodox Shas party has said it will quit the government if the division of Jerusalem between Israel and the Palestinians is broached.
The Palestinians want mostly Arab east Jerusalem, which Israel seized in the 1967 Arab-Israeli war, as the capital of their future state.