Actually both of the major candidates, Benjamin Netanyahu and his chief competitor, Isaac Herzog, are claiming to have had a victorious election. However, the likely outcome now that the main opposition party, the Zionist Union, has failed to secure a sure victory, is that Netanyahu will continue as the Prime Minister. The likeliest outcome is that he will move to the right to shore up the majority of seats in the Knesset and assure that he will continue as Prime Minister.
The most important name in this election may well be Moshe Kahlon, who is the leader of Koolanu, which is a center-right party but had teamed up with the left leading into this election in an effort to unseat Netanyahu. Now that that has failed, members of the right hope that with enough incentive, Kahlon will move back to the right to ensure a center-right government.
This is a big victory for Netanyahu and Likud, who were thought to be finished after late polling showed they had fallen significantly behind. However, it seems that the poll numbers were wrong and Netanyahu was able to do enough in the end to draw voters back to the right.