Earlier, he told his Cabinet that he was stepping down.
Channel 10 TV broadcast a government picture of Olmert reading his letter of resignation to Peres Sunday evening.
Foreign Minister Tzipi Livni is already meeting with party leaders to set up a new coalition government. Peres is meeting with party leaders to decide on Olmert's successor, but Livni is the obvious choice. She supports Olmert's efforts toward a peace accord with the Palestinians. She won a party primary election last week.
Livni won that race last week by a narrow margin, but that victory did not assure her the premiership. Peres must first assign her the task of trying to cobble together a government, giving her six weeks to forge a coalition. Should she fail, parliamentary elections would be called for early 2009, a year and a half ahead of schedule.
Olmert is expected to stay on as caretaker prime minister until a successor is in place.
At the weekly Cabinet meeting on Sunday, Olmert notified ministers of his intention to resign, pledging to help Livni "with all my might to form a government."
Over the weekend, Livni met with potential coalition partners, including two small factions that are not part of the current government, which controls 67 of parliament's 120 seats.
Any accords that might emerge from talks with the Palestinians and recently renewed, indirect negotiations with Syria would benefit from broad-based parliamentary backing.
Neither Kadima nor its coalition partners appear eager for a new election, fearing they would be ousted from power. But the ultra-Orthodox Shas Party, which could be key to building a new coalition, has already said it would not join a government willing to share Jerusalem with the Palestinians.
As lead peace negotiator, Livni is committed to discussing all the outstanding issues between Israel and the Palestinians. The fate of Jerusalem, whose eastern sector the Palestinians claim for a future state, is at the core of the conflict.
Polls show that in the event of an election, Kadima would be in a tight race with the hawkish Likud Party, headed by opposition leader Benjamin Netanyahu, a former prime minister.
Livni would be expected as prime minister to pursue a moderate and pragmatic course in peacemaking with the Palestinians and Syria. Netanyahu takes a tougher line in peace talks, and Israel's relations with the Arab world suffered when he was prime minister in the late 1990s.
Kadima was founded in 2005 by then-Prime Minister Ariel Sharon.
But Sharon suffered a debilitating stroke in early 2006, pushing Olmert into the leadership role.
Olmert led Kadima to victory in 2006 parliamentary elections.
But his term in office was troubled by a series of police investigations, Israel's inconclusive 2006 war against Lebanese Hezbollah guerrillas and months of peace talks with the Palestinians that have yielded no breakthroughs.
The police investigations focus on Olmert's financial dealings in the years before he became prime minister. Police have recommended he be indicted on counts that include bribery and money laundering, but prosecutors have not decided whether to press charges. Olmert denies any wrongdoing.