"Tomorrow, I will begin meeting with representatives of the factions in order to form quickly a coalition that can deal with all of the challenges that lie ahead," she said.
Livni received 43.1% of the vote, 2% ahead her main rival, Transport Minister Shaul Mofaz, becoming Kadima's first woman and only its third leader since former prime minister Ariel Sharon founded the party in November 2005.
She said the national mission "is to create stability quickly."
Current premier Ehud Olmert, who faces corruption and fraud charges, has pledged to resign as soon as the new party leader is chosen. However, he is to stay on as caretaker prime minister until a new coalition government has been formed.