The new law, a ministerial compromise following a bill initiated by Elazar Stern of Justice Minister Tzipi Livni's HaTnuah movement, stipulates that the chief rabbi of each Israeli city would be able to form and head a conversion court, pending conditions to be set by the chief rabbinate.
This would potentially greatly increase the number of conversion courts from the four current state-recognised Orthodox bodies.
Israel has some 364,000 citizens defined as "religionless," the bulk of whom immigrated from the former Soviet Union.
They are not considered Jewish under the strict definition of Jewish law, despite most having lineage of the religion, but they are still considered Israeli by the state.
Stern pledged to act swiftly to implement the decision and form new courts for conversion candidates, "especially those who had already given up on conversion."
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Livni called the new law "great news for hundreds of thousands of citizens who live with us, whom we encouraged to immigrate as part of the Law of Return but until now were second-rate citizens."
Critics say Israel's conversion courts, overseen by the ultra-Orthodox chief rabbinate, are overly stringent and discourage potential converts.
The chief rabbinate, however, has not accepted the new law, and will discuss its course of action later, a spokesman said.
Natan Sharansky, chairman of Israel's Jewish Agency, which links Jewish communities around the world with Israel and each other, said the new law was "crucial to the successful absorption and integration of many immigrant Israelis."
"There is no doubt that this is a welcome development to all who wish to draw in those who are distant and embrace those who have come near," he said in a statement.
Rabbi Seth Farber, whose ITIM organisation provides advice and help to people challenged by Israel's religious bureaucracy, hailed the law as "the first major reform in religion and state that has the potential to fundamentally change the status quo in Israel."