In his victory speech he told moderate Palestinian leader Mahmoud Abbas that he is ready to strike a deal, but also claimed a mandate to draw up Israel's final borders.
Mr Abbas urged Mr Olmert to abandon those plans, speaking to reporters in the Sudanese capital Khartoum, where he is attending an Arab summit.
"The result was expected. But what is more important now is that Olmert changes his agenda and abandon his unilateral plans to fix the borders," he said.
Mr Olmert also announced he would not deal with Islamic radicals Hamas, who won a landslide victory over Mr Abbas' mainstream Fatah party in January's Palestinian parliamentary elections.
The Kadima party, only four months old, gained 28 seats, the most in the 120-seat Knesset.
The party was formed by ailing Prime Minister Ariel Sharon late last year when he broke away from the Likud party over wrangling over his Gaza disengagement plan.
Likud gained just 11 seats, in fifth place.
Mr Olmert will have to find coalition partners in order to govern, most likely with the centre-left Labour party, which gained 20 seats and came in as the second most popular party.
Other smaller parties, including the dovish Meretz and the Pensioners' List, which won around seven seats in a surprise, are likely to be invited into the coalition.
Victory speech
While warning that the Jewish state is ready to determine borders on its own terms, Mr Olmert said he os ready to compromise and would prefer to reach a negotiated settlement.
"We will strive to bring about the establishment of the final borders of Israel as a Jewish state with a permanent Jewish majority, and as a democratic country," he told Kadima activists.
"We will work to do this through negotiations, through an agreement with our Palestinian neighbours... There is no good alternative to a peace agreement."
Mr Olmert said it is time for the Palestinian leadership to follow the example of other Arab leaders who have made peace with Israel and display a willingness to compromise.
Incoming Palestinian prime minister Ismail Haniya of Hamas said the people of the West Bank and Gaza Strip would never accept a new map unilaterally drawn up by Israel.
Palestinians said such actions would uproot tens of thousands of settlers while tracing a border along a fortified barrier that Israel is building inside the West Bank would deny them a viable state.
Mr Olmert used his victory speech to flag his plans, saying Israel is also willing to take its destiny into its own hands in the absence of a partner for peace.
"I call on the head of the Palestinian Authority Mahmoud Abbas, I am telling him directly that during thousands of year we had a dream of peace in Israel, this land and its historic borders will always remain the wish in our hearts.
"But understand. We are ready to make compromises, to give up parts of beloved land of Israel where our sons are buried and evacuate Jews who live there to make a life to fulfil your dream to live in peace.
"If the Palestinians react in the near future, we will return to the negotiating table. If they don't do so, Israel will take its fate into its own hands."
Mr Olmert said that in the absence of negotiations with the Palestinians, his next government would seek the support of the United States for his policy of acting unilaterally.
Voter turnout for the election was 62.3 percent, the lowest in history and almost six percent down on the previous election in 2003.