The law of Return was passed on July 5, 1950, granting every Jew a right to come to Israel as an “oleh” – new immigrant. It excludes those who are engaged in an activity directed against the Jewish people or are likely to endanger public health or the security of the State. It also states that a Jew who has come to Israel and subsequent to his arrival has expressed his desire to settle in Israel may – while still in Israel – apply for citizenship.
In 1954 amendment of the law a paragraph was added to the paragraph about the restriction of immigration: the applicant cannot receive a new immigrant visa if he/she is a person with a criminal past and is likely to endanger public welfare.
In 1970 amendment the right to return to Israel was extended to a child and a grandchild of a Jew, the spouse of a Jew, the spouse of a child of a Jew and the spouse of a grandchild of a Jew, except for a person who has been a Jew and has voluntarily changed his religion. This amendment gave also the definition of a Jew: "Jew" means a person who was born of a Jewish mother or has become converted to Judaism and who is not a member of another religion.
The full text of the Law of Return and its amendments can be found here.