The victory puts her one step closer to becoming Israel's next prime minister and only the second female premier, preceded by Golda Meir, whose term ended nearly 35 years ago.
Ms. Livni won the Kadima primaries with roughly 48 percent of the vote, exit polls from three different television channels predicted after polling stations closed at 10:30 p.m. on Wednesday. She beat her strongest competitor, Shaul Mofaz, by a margin of about 10 percent.
Livni will replace Ehud Olmert, who promised that he would leave office the day after party primaries were held, following demands he resign due to his likely indictment on corruption charges.
"A lot is dependent on her," Knesset member Ofer Pines told Israel's Channel One as the results came in. "If she can bring in new hope to the party and to the country, that would be great. If not, it's a real missed opportunity."
Mr. Olmert has headed Kadima since January 2006 when he took over after the party's founder, Ariel Sharon, was incapacitated by a major stroke. Both Olmert and Livni were all originally members of the right-wing Likud Party, but followed Mr. Sharon when he left to form Kadima as a centrist party with "disengagement" – Israel's departure from the Gaza Strip and a few West Bank settlements in August 2005 – at the center of its unilateralist agenda.
Livni, who has led Israel's negotiations with the Palestinians since the peace process was revamped by the Bush administration in Annapolis, Md., last November, is seen as being far keener on making peace with Israel's neighbors. Although they are in the same party, Livni's outlook on international affairs is markedly different from that of Mr. Mofaz, a military hawk and former army chief of staff who has taken a much more aggressive line on Iran's nuclear program.
Livni's parents were members of the Irgun, one of the most hard-line Zionist militias at the time of Israel's founding. Trained as a lawyer, she served in the Mossad, Israel's spy agency, before being elected to the Knesset in 1999.