Prime Minister Benjamin Netanyahu's Likud party said on Thursday night it had agreed with its partners in the vulnerable coalition government that 1,300 Ethiopians would come this year and more would be considered later.
Ethiopian Israelis staged a protest march in Jerusalem last month after the government cancelled plans to allow their relatives to join them, citing budgetary constraints.
The people in question are members of a community known as Falash Mura, descendants of Ethiopian Jews who converted to Christianity, many under duress, in the 18th and 19th centuries.
Two Likud lawmakers had announced that in protest they would no longer vote for the government in the Knesset, where it already held only a knife-edge majority of one seat in the 120-member legislature.
Since then the government has postponed several draft bills for fear that they would be voted down.
But the boycott by Ethiopian-born lawmaker Avraham Neguise and parliamentary interior committee chairman David Amsalem threatened its very survival.
Failure to win a majority in this summer's budget debate would automatically trigger its resignation.
The maverick parliamentarians on Friday welcomed the coalition's change of heart.
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"We are very pleased. The prime minister has carried out an act of historic justice," Neguise told Israeli public radio.
"We are very happy that our brothers will arrive."
Amsalem said Netanyahu's previous decision was based on misinformation about the true scale and cost of resettling the Falash Mura.
"When we sat down and explained to him and showed him the real data he understood that the issue is a just one and doesn't exactly cost what was said," he told the radio.
"It's a matter of bringing fewer than 9,000 Jews."
He did not answer when asked if Netanyahu had relented purely as a matter of political survival, but commentator Yuval Karni, writing in Hebrew daily Maariv, had no doubt.
"As soon as he realised that these two MPs were serious he realised that his seat was in danger and gave them everything," he said.
"If necessary he would have brought all of Addis Ababa to Israel."
Israel's Ethiopian community numbers around 135,000 people. Most of them arrived between 1984 and 1991 under the Law of Return, which guarantees citizenship to all Jews.
It does not, however, apply to the Falash Mura.