"When we receive the mandate... I shall serve as prime minister for the first two years and Tzipi Livni will serve as prime minister for the second half" of the four-year term, Hertzog said at a televised news conference.
"Today the Zionist centre has risen against the parties of the extreme right," said Livni, formerly Israel's chief peace negotiator with the Palestinians, who was fired from government last week by Prime Minister Benjamin Netanyahu, who accused her of working against his right-leaning coalition from within.
She began her political career in Likud before following the late Ariel Sharon when he founded the Kadima party, then setting up her own HaTnuah before the last election.
She said that today's Likud has been taken over by the far-right.
"The extremists... are turning our country into an isolated state, closed and alienated from its own citizens."
"I am here to produce the force-multiplier that will replace the government of Israel," she said.
Polls published on Tuesday said an alliance between Labour and Livni's HaTnuah party could nudge Netanyahu's Likud from power.
A survey by parliament TV, published by Maariv newspaper, said that a partnership could win 23 seats in the 120-member Knesset, while Likud was projected to win 21.
Another poll by news website Globes put the figure at 24 for Labour-HaTnuah and 23 for Netanyahu's party.
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Likud said the new alliance, if it took power, would make sweeping concessions in talks with Palestinian leader Mahmud Abbas, who is also known as Abu Mazen.
"Livni's alliance with Herzog is Abu Mazen's dream team," said the party's central committee which met Wednesday in the West bank settlement of Ariel.
"There is no doubt what he could expect from such a radical left-wing government; dangerous concessions in Jerusalem and throughout our homeland," Likud said in a statement.
Netanyahu fired Livni and Finance Minister Yair Lapid, head of the centrist Yesh Atid party, before calling an early election, which parliament set for March 17.
Livni said that HaTnuah and labour would field a joint list of candidates and that she expected unnamed other parties to enter the alliance.
The same tactic was used in the 2013 election when Likud and Foreign Minister Avigdor Lieberman's Israel Beitenu ran on a joint ticket, taking 31 seats.
A bill passed in March raising the number of votes which parties need to enter parliament under Israel's proportional representation system could see more parties banding together to cross the new threshold.
A rotating premiership is also not a new idea.
Following a political deadlock after the 1984 election, the two largest parties agreed that Labour's Shimon Peres would hold the premiership for the first two years and Likud's Yitzhak Shamir for the next two.
Media reported Wednesday evening that popular former Likud minister Moshe Kahlon, who last month announced a comeback at the head of a new party, has named it "Kulanu" (All Of Us).
Polls have predicted it could win up to 13 seats.