They approved a revised government proposal to relocate by a vote of 45 for and 29 against, a spokesperson wrote on the outpost's Twitter account.
The 40 families living at Amona in the northern West Bank faced a Supreme Court order to leave the site by December 25 because it was found to have been built on private Palestinian land.
The dispute over whether to demolish the outpost northeast of Ramallah has taken on international importance because of concern over settlement expansion in the West Bank, occupied by Israel since 1967.
Despite the prospect of forceable eviction by the army, the Amona residents had turned down a compromise deal on Thursday aimed at meeting their objections while also obeying the court ruling.
Vowing "passive resistance", residents had been fortifying the outpost since then, building barricades, drilling into floors and welding obstacles, an AFP reporter said.
Hundreds of non-residents joined them in solidarity, they said.
Today, they were offered a new deal after an all-night meeting with Prime Minister Benjamin Netanyahu.
He has been seeking a way out of an impasse which has put him between the court and the legal opinion of his own attorney general on one hand, and the anger of settlers who are a key part of his political constituency on the other.
Netanyahu will now need to go back to the court and ask for a stay of execution, probably 30 days, for the new plan to be implemented.
Baruch Marzel, a hardline nationalist and follower of the late racist rabbi Meir Kahane, said the Amona settlers should not have accepted Netanyahu's offer.
Residents also had mixed feelings, with some protest leaders speaking out against the deal to applause from the youngsters.
Others simply drifted quietly away from the site.
Tweets from a settlement spokesman gave no details of the offer, but the head of the Amona "struggle committee" said it was an improvement on the previous proposal.
"I think that this draft is better, very much better, than the previous one presented to us," he told Israeli army radio, without elaborating.
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