Kadima’s recently-elected leader, Shaul Mofaz, is set to be named deputy PM.
PM Benjamin Netanyahu said their new coalition wanted a “responsible” peace process with the Palestinians and “serious” talks about Iran’s nuclear programme.
The move came as parliament debated its dissolution before an election Benjamin Netanyahu had planned for September.
Kadima is currently the biggest party in the Knesset, but recent polls have suggested the number of seats it holds could be halved.
The new coalition will have a majority of 94 – one of the biggest in Israeli history.
President Shimon Peres welcomed the deal as “good for the people of Israel”.
According to an outline of the deal, Kadima would back Benjamin Netanyahu’s Likud party in return for changes to the so-called Tal Law, which allows ultra-Orthodox Jewish seminary students to defer military conscription.
It was declared unconstitutional by the Supreme Court in February.
Secularists say the Tal Law is unfair, but small religious parties – which are crucial to Benjamin Netanyahu’s present coalition – want ultra-Orthodox youths to continue to be allowed to opt for religious study over military service.
Labour party leader Shelly Yachimovich has condemned the deal, saying it is a “pact of cowards.”
“This is the most ridiculous zigzag in the history of Israeli politics,” she wrote on her Facebook page.
Four months ago Shaul Mofaz publicly called Benjamin Netanyahu a “liar”, saying he had leaked an inaccurate quote in his name.
In March, he publicly pledged never to join Benjamin Netanyahu’s government.
In addition to becoming vice PM, Shaul Mofaz will also join Netanyahu’s inner circle – previously known as the Forum of Eight, and will become a member of the security cabinet.
Benjamin Netanyahu’s right-wing administration had been scheduled to remain in power until October 2013.
He earlier announced plans to bring elections forward after disagreements with a junior coalition partner.
Opinion polls suggest Likud could win at least a quarter of the Knesset’s 120 seats if the elections were held in the autumn.
The polls are not very accurate or trustworthy in Israel, but Benjamin Netanyahu is, by some stretch, the most popular politician.
Benjamin Netanyahu must be credited with leading one of the country’s most stable governments of recent times.
He says the main issues in any election would be, as ever, security, including now the threat from Iran, and relations with the Palestinians.
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