Prime Minister Sharon made the offer in a call to Labour leader Shimon Peres, his old ideological rival, after the rightist Likud's Central Committee voted on Thursday to overturn its earlier ban on negotiating an alliance.
It was a major blow for hardline Likud rebels, who oppose giving up Gaza or any land occupied since the 1967 Middle East war. They tried to prevent a partnership with pro-withdrawal Labour as a way to stop the planned pullout.
Labour's entry into Sharon's shaky coalition could help restart long-stalled peace talks after Palestinians elect a successor to the late Yasir Arafat on 9 January.
Peres praised Likud's decision to team up with his centre-left party. Labour's leadership planned to meet on Saturday night to grant its approval, and coalition building was expected to begin on Sunday.
Sharon needs support for his
Gaza withdrawal plan
"It's a foregone conclusion. It will take 10 days to two weeks to form a government," a Sharon confidant said.
Sharon needs Labour to help restore his parliamentary majority and carry out his plan to "disengage" by evacuating all 21 settlements in Gaza and four out of 120 in the West Bank by the end of next year.
While many Likud members are uneasy about bringing Labour into government, the executive - voting 62% to 38% in favour - showed few had an appetite for forcing elections nearly two years ahead of schedule, which would have been the alternative.
Polls show most Israelis favour parting with impoverished Gaza, but hardliners call any pullout a "reward for terrorism".
Palestinians fear it is a ruse to cement Israel's hold on the West Bank, where the vast majority of settlers live.
"We hope formation of a new Israeli government will lead to revival of the peace process that will end Israeli occupation and realise a two-state solution," Palestinian cabinet minister Saib Uraiqat said.
"I am struggling to achieve a national unity government - nothing else"
Labour leader Shimon Peres
On the Israeli political front, Sharon's coalition has been whittled down to a minority government with 40 seats in the 120-member parliament.
Labour, with control of 22 seats, is needed to help pass the budget and avoid automatic elections.
Though Peres is eager to join, haggling over cabinet portfolios and differences over the budget could slow the process.
Likud's approval for coalition talks with two ultra-Orthodox parties could also create problems.
"I am struggling to achieve a national unity government -nothing else," Peres said. "Everything else is trivial."
Wajih Kayuf, a member of the Labour Party, told Aljazeera the coalition would be a troubled one.
"The electoral battle Sharon has won inside his party ... allows him to go into negotiation with the Labour Party and other opposition parties," he said.
But he added: "The coalition will face many problems.
"The only explanation behind the forming of the coalition with the Likud was to help Sharon achieve his plan to withdraw from the Gaza Strip."