Any Jewish person is eligible for Israeli citizenship.
Every Jew on Earth is technically eligible for Israeli citizenship as defined by the Law of Return 5710-1950. Interestingly, there are very few limitations. The first requirement, obviously, is that the person must be Jewish. Once that is determined there are only two rules that deny citizenship. The first is if the person “is engaged in an activity directed against the Jewish people,” and the second is if they are, “likely to endanger public health or the security of the State.”
So as long as you’re Jewish and not deemed a national security threat, Israel is a pretty open terrain. How did this law come to be? Israel was not formally established until after World War II at the General Assembly of the United Nations on 29 November 1947. The very next day Israel was invaded by neighboring Arab states in support of the Palestinians who occupy the same land. Since then an unending war has been taking place. In fact, every Jewish citizen is mandated to serve in the army to combat the threat they face.
In an attempt to rally scattered Jewish populations around the globe, Israel made the rule that any Jewish person could move there, and no doubt to ensure their safety and the continuity of their state.