The remaining members of the Ethiopian Jewish community are to move to Israel.
After years of wrangling, Israel’s cabinet voted in favour of giving the more than 7,800 Falash Mura Jews citizenship.
The decision, likely to be the final chapter in the saga of the Ethiopian Jewish community, comes almost exactly 26 years after Operation Moses, when Israel airlifted 8,000 Jews out of Ethiopia in secret.
A further 14,000 came to Israel in 1990 on a second airlift, with many more arriving independently.
But the aliyah of the final members of the Ethiopian Jewish community has been problematic because of questions over their Jewish origin.
Of the 85,000 Ethiopian Jews in Israel, nearly half are Falash Mura Jews, descendants of the Beta Israel group who converted to Christianity a century ago.
They claimed the conversion was forced and that as a community they maintained Jewish traditions, but some Israeli politicians argued they wanted to make aliyah only to escape from Ethiopia.
Israeli rabbis ultimately ruled that the Falash Mura were of Jewish descent, enabling them to enter Israel on condition that they re-converted to Orthodox Judaism. But in August 2008 the government announced that the immigration of the Falash Mura was to end.
That decision was reversed in December 2009 and the cabinet has now approved a plan to bring the last of the Falash Mura to Israel over the next four years.
At present, most of the community is living in temporary shelters in the Ethiopian city of Gondar.
Prime Minister Benjamin Netanyahu said: “We have a moral commitment as Jews, as the people of Israel, to find a solution.”
The Public Committee for the Remainder of the Ethiopian Jews said: “This is an ethical, Jewish, humanitarian and Zionist decision to bring justice to those Jewish brothers still waiting to return and connect to the Jewish people in its land.”
The Jewish Agency, which has petitioned for Israel to give the Falash Mura citizenship, has pledged £2.9 million to help absorb the community into Israeli society.