Exit polls showed Kadima getting about 30 of the seats in the 120-member Knesset, more than any other party and enough to form the basis of a ruling coalition though less than opinion polls had predicted.
Olmert told party loyalists gathered to celebrate that he hoped it would still be possible to set a border through negotiations with the Palestinians, but that Israel would act alone if peace efforts remained stalled.
"This evening, a very important chapter has ended in the history of the country. We, with me at your head, must shape the new chapter in the history of Israel," he said.
"We are ready to compromise, to give up parts of the beloved land of Israel ... and evacuate, under great pain, Jews living there, in order to create the conditions that will enable you to fulfil your dream and live alongside us," he said in words addressed to Mahmoud Abbas, the Palestinian president.
"If the Palestinians are wise enough to act, then in the near future we will sit together at the negotiating table to create a new reality. If they do not, Israel will take its destiny in hand ... the time has come to act."
Earlier surveys, issued by Israeli media after voting ended on Tuesday, gave centrist Kadima 29 to 32 seats in the 120-member parliament, putting it in a good position to form a coalition government, with 20 to 22 seats going to centre-left Labour and 12 to the right-wing Likud.
The far-right Yisrael Beiteinu party was projected by two exit polls to get 14 seats, beating Likud.
Olmert has been promoting a plan to impose a border on the Palestinians by dismantling isolated Jewish settlements in the West Bank by 2010 and expanding bigger blocs in the territory. The World Court has ruled that all of the 145 settlements Israel has built on occupied territory are illegal. Israel disputes this.
Approval of consolidation
For Olmert, victory would mean approval of "consolidation", his term for the unilateral steps he plans should Hamas refuse to recognise Israel, disarm and accept interim peace accords.
Olmert's policy of imposing Israel's borders on its own terms ignores an international peace "road map", which envisaged a cessation of violence and the start of mutual steps leading to the creation of a Palestinian state alongside a secure Israel.
Ariel Sharon founded Kadima last November after deserting Likud, where far-right members revolted over the Gaza withdrawal. He suffered a stroke in January and fell into a coma.